4つの4(v2)(失敗)


時事ネタ.(もう流行りは過ぎた.)
なるしす さんの4つの4で1~100を作ろう(以下URL)が流行っている.よって便乗した.の4回目.
http://www.nicovideo.jp/watch/sm27096518

・4を4つ使ってできる自然数はどんなものがあるか?を調べた.

・使える2項演算子は次のようにした.
(x+y)
(x-y)
(x\times y)
(\frac{x}{y})
(x^y)

・使える1項演算子は次のようにした.
(x!)(ただし、(x=3,4)の場合に限る)
(\sqrt{x})(ただし、(x>0)の場合に限る)

また、1項演算子の連続した使用は3度までとする.

・4を使用した定数として次のものが使える.
(44,444,4444) (4を並べて使う)
(.4)(小数点を省略)
(.\dot{4})(循環小数)((=\frac{4}{9}))

さらに、計算機の性能の制限が次のようにあるとする.
計算過程において,(100000)を超えた場合、これを捨てる.

TODO:計算の途中において、絶対値が1より小さい数を44乗すると0と誤認識する問題がある.

以上の条件で可能な(100000)以下の正の整数は次の通りである.(間違いを含む)
計算アルゴリズムを少し変更して、簡単な式がだいたい出てくるようにしました(見やすい).

[ 0 = 44-44 ]
[ 1 = \frac{44}{44} ]
[ 2 = \frac{4}{\left(4+4\right)}\times4 ]
[ 3 = \sqrt{\sqrt{\sqrt{{\frac{\left(4-.4\right)}{.4}}^{4}}}} ]
[ 4 = 4+{.4}^{44} (間違っている)]
[ 5 = \frac{\left(4+\left(4\times4\right)\right)}{4} ]
[ 6 = 4+\frac{\left(4+4\right)}{4} ]
[ 7 = \frac{44}{4}-4 ]
[ 8 = \left(4+4\right)+\left(4-4\right) ]
[ 9 = \left(\frac{4}{4}+4\right)+4 ]
[ 10 = \frac{\left(44-4\right)}{4} ]
[ 11 = \frac{44}{\sqrt{\left(4\times4\right)}} ]
[ 12 = \frac{\left(44+4\right)}{4} ]
[ 13 = \frac{44}{4}+\sqrt{4} ]
[ 14 = \left(4\times\left(4-.4\right)\right)-.4 ]
[ 15 = \frac{44}{4}+4 ]
[ 16 = \left(44-4\right)\times.4 ]
[ 17 = \left(4\times4\right)+\frac{4}{4} ]
[ 18 = \left(44\times.4\right)+.4 ]
[ 19 = \frac{\left(\left(4+4\right)+.\dot{4}\right)}{.\dot{4}} ]
[ 20 = .\dot{4}+\left(44\times.\dot{4}\right) ]
[ 21 = \frac{\left(.4+\left(4+4\right)\right)}{.4} ]
[ 22 = \frac{44}{4}\times\sqrt{4} ]
[ 23 = \frac{\left(\left(4!\times4\right)-4\right)}{4} ]
[ 24 = \left(4+\left(4\times4\right)\right)+4 ]
[ 25 = \left(4\times4\right)+\frac{4}{.\dot{4}} ]
[ 26 = \frac{44}{\sqrt{4}}+4 ]
[ 27 = \frac{\left(4+\left(4+4\right)\right)}{.\dot{4}} ]
[ 28 = 44-\left(4\times4\right) ]
[ 29 = \frac{4}{\left(.4\times.4\right)}+4 ]
[ 30 = \frac{\left(4+\left(4+4\right)\right)}{.4} ]
[ 31 = 4+\frac{4!}{\left(.\dot{4}+.\dot{4}\right)} ]
[ 32 = \left(4\times4\right)+\left(4\times4\right) ]
[ 33 = \frac{44}{\sqrt{\left(4\times.\dot{4}\right)}} ]
[ 34 = 44-\frac{4}{.4} ]
[ 35 = 44-\frac{4}{.\dot{4}} ]
[ 36 = 44-\left(4+4\right) ]
[ 37 = \frac{\left(\left(4\times4\right)+.\dot{4}\right)}{.\dot{4}} ]
[ 38 = 44-\left(4+\sqrt{4}\right) ]
[ 39 = 44-\frac{\sqrt{4}}{.4} ]
[ 40 = 44-\sqrt{\left(4\times4\right)} ]
[ 41 = \frac{\left(\left(4\times4\right)+.4\right)}{.4} ]
[ 42 = \left(\sqrt{4}+44\right)-4 ]
[ 43 = 44-\frac{4}{4} ]
[ 44 = \left(44-4\right)+4 ]
[ 45 = 44+\frac{4}{4} ]
[ 46 = \left(44-\sqrt{4}\right)+4 ]
[ 47 = \sqrt{\frac{4}{.\dot{4}}}+44 ]
[ 48 = 4\times\left(4+\left(4+4\right)\right) ]
[ 49 = \frac{\sqrt{4}}{.4}+44 ]
[ 50 = \left(\sqrt{4}+44\right)+4 ]
[ 51 = \frac{\left(4!+.\dot{4}\right)}{.\dot{4}}-4 ]
[ 52 = 4+\left(44+4\right) ]
[ 53 = 44+\frac{4}{.\dot{4}} ]
[ 54 = \frac{4}{.4}+44 ]
[ 55 = \frac{44}{\left(.4+.4\right)} ]
[ 56 = 4\times\left(\frac{4}{.4}+4\right) ]
[ 57 = \frac{\left(4!-.\dot{4}\right)}{.\dot{4}}+4 ]
[ 58 = \frac{\left({4}^{4}-4!\right)}{4} ]
[ 59 = \frac{\left(4!+4\right)}{.\dot{4}}-4 ]
[ 60 = \left(4\times4\right)+44 ]
[ 61 = \frac{4}{4}+\frac{4!}{.4} ]
[ 62 = \frac{44}{\sqrt{.\dot{4}}}-4 ]
[ 63 = \frac{\left({4}^{4}-4\right)}{4} ]
[ 64 = \left(4+4\right)\times\left(4+4\right) ]
[ 65 = \frac{\left({4}^{4}+4\right)}{4} ]
[ 66 = \frac{44}{.\dot{4}}\times\sqrt{.\dot{4}} ]
[ 67 = 4+\frac{\left(4!+4\right)}{.\dot{4}} ]
[ 68 = 4+\left(4\times\left(4\times4\right)\right) ]
[ 69 = \frac{\left(\left(4!+4\right)-.4\right)}{.4} ]
[ 70 = 4+\frac{44}{\sqrt{.\dot{4}}} ]
[ 71 = \frac{\left(\left(.4+4\right)+4!\right)}{.4} ]
[ 72 = \left(44+4\right)+4! ]
[ 73 = \frac{\left(\sqrt{.\dot{4}}+\left(4!\times\sqrt{4}\right)\right)}{\sqrt{.\dot{4}}} ]
[ 74 = \frac{\left(4!+4\right)}{.4}+4 ]
[ 75 = \frac{44}{.\dot{4}}-4! ]
[ 76 = \left(\left(4!-4\right)\times4\right)-4 ]
[ 77 = \sqrt{{\frac{4}{.\dot{4}}}^{4}}-4 ]
[ 78 = \left(\left(4!-4\right)\times4\right)-\sqrt{4} ]
[ 79 = \frac{\left(4!+.\dot{4}\right)}{.\dot{4}}+4! ]
[ 80 = \left(4+\left(4\times4\right)\right)\times4 ]
[ 81 = \frac{\left(4\times4\right)}{\left(.\dot{4}\times.\dot{4}\right)} ]
[ 82 = \left(\left(4!-4\right)\times4\right)+\sqrt{4} ]
[ 83 = \frac{\left(4!-.4\right)}{.4}+4! ]
[ 84 = \left(44\times\sqrt{4}\right)-4 ]
[ 85 = {\frac{4}{.\dot{4}}}^{\sqrt{4}}+4 ]
[ 86 = \frac{44}{.4}-4! ]
[ 87 = \left(4!\times4\right)-\frac{4}{.\dot{4}} ]
[ 88 = 44+44 ]
[ 89 = \frac{\left(\frac{4!}{\sqrt{.\dot{4}}}-.4\right)}{.4} ]
[ 90 = \frac{\left(44-4\right)}{.\dot{4}} ]
[ 91 = \left(4!\times4\right)-\frac{\sqrt{4}}{.4} ]
[ 92 = \left(44\times\sqrt{4}\right)+4 ]
[ 93 = \left(4!\times4\right)-\sqrt{\frac{4}{.\dot{4}}} ]
[ 94 = \frac{4}{\left(.\dot{4}-.4\right)}+4 ]
[ 95 = \frac{44}{.\dot{4}}-4 ]
[ 96 = \left(44+4\right)\times\sqrt{4} ]
[ 97 = \frac{44}{.\dot{4}}-\sqrt{4} ]
[ 98 = \frac{\left(44-.\dot{4}\right)}{.\dot{4}} ]
[ 99 = \frac{\left(.4+4\right)}{\left(.\dot{4}-.4\right)} ]
[ 100 = \frac{\left(44-4\right)}{.4} ]
[ 101 = \frac{44}{.\dot{4}}+\sqrt{4} ]
[ 102 = \left({4}^{4}\times.4\right)-.4 ]
[ 103 = 4+\frac{44}{.\dot{4}} ]
[ 104 = .4\times\left({4}^{4}+4\right) ]
[ 105 = \frac{\left(44-\sqrt{4}\right)}{.4} ]
[ 106 = \frac{44}{.4}-4 ]
[ 107 = \frac{\left(4!-\left(.\dot{4}-4!\right)\right)}{.\dot{4}} ]
[ 108 = \frac{\left(44+4\right)}{.\dot{4}} ]
[ 109 = \frac{\left(44-.4\right)}{.4} ]
[ 110 = \frac{44}{\sqrt{\left(.4\times.4\right)}} ]
[ 111 = \frac{444}{4} ]
[ 112 = \left({4}^{4}-4\right)\times.\dot{4} ]
[ 114 = \frac{44}{.4}+4 ]
[ 115 = \frac{\left(\sqrt{4}+44\right)}{.4} ]
[ 116 = \left(\left(4!+4\right)\times4\right)+4 ]
[ 117 = \frac{\left(\left(4!\times\sqrt{4}\right)+4\right)}{.\dot{4}} ]
[ 118 = \left(4!-.4\right)\times\frac{\sqrt{4}}{.4} ]
[ 119 = \frac{\left(4!-\left(.4-4!\right)\right)}{.4} ]
[ 120 = \frac{\left(44+4\right)}{.4} ]
[ 121 = \sqrt{{\frac{44}{4}}^{4}} ]
[ 122 = \frac{\sqrt{4}}{.4}\times\left(4!+.4\right) ]
[ 123 = \frac{44}{.\dot{4}}+4! ]
[ 124 = \frac{{4}^{4}}{\sqrt{4}}-4 ]
[ 125 = \frac{\left(4!-4\right)}{\left(.4\times.4\right)} ]
[ 126 = \frac{\left({4}^{4}-4\right)}{\sqrt{4}} ]
[ 127 = \frac{\left({4}^{4}-\sqrt{4}\right)}{\sqrt{4}} ]
[ 128 = \left(4\times4\right)\times\left(4+4\right) ]
[ 129 = \frac{\left({4}^{4}+\sqrt{4}\right)}{\sqrt{4}} ]
[ 130 = \frac{\left({4}^{4}+4\right)}{\sqrt{4}} ]
[ 131 = \frac{4!}{\left(.\dot{4}\times.4\right)}-4 ]
[ 132 = 44\times\sqrt{\frac{4}{.\dot{4}}} ]
[ 133 = \frac{4!}{\left(.\dot{4}\times.4\right)}-\sqrt{4} ]
[ 134 = \frac{44}{.4}+4! ]
[ 135 = \frac{4!}{\left(4\times\left(.\dot{4}-.4\right)\right)} ]
[ 136 = \sqrt{4}\times\left(44+4!\right) ]
[ 137 = \sqrt{4}+\frac{4!}{\left(.\dot{4}\times.4\right)} ]
[ 138 = \frac{\left(\left(4!\times4\right)-4\right)}{\sqrt{.\dot{4}}} ]
[ 139 = 4+\frac{4!}{\left(.\dot{4}\times.4\right)} ]
[ 140 = 44+\left(4!\times4\right) ]
[ 141 = \frac{\left(\left(4!\times4\right)-\sqrt{4}\right)}{\sqrt{.\dot{4}}} ]
[ 142 = \left(\left(4+\sqrt{4}\right)\times4!\right)-\sqrt{4} ]
[ 143 = \frac{\left(\left(4!\times4!\right)-4\right)}{4} ]
[ 144 = \frac{\left(4\times\left(4\times4\right)\right)}{.\dot{4}} ]
[ 145 = \frac{\left(4+\frac{4!}{.\dot{4}}\right)}{.4} ]
[ 146 = \frac{4!}{\left(.4\times.4\right)}-4 ]
[ 147 = \frac{\left(\left(4!\times4\right)+\sqrt{4}\right)}{\sqrt{.\dot{4}}} ]
[ 148 = 4+\left(\left(4+\sqrt{4}\right)\times4!\right) ]
[ 149 = \frac{\left(\frac{4!}{.4}-.4\right)}{.4} ]
[ 150 = \frac{4!}{.\dot{4}}+\left(4!\times4\right) ]
[ 151 = \frac{\left(.4+\frac{4!}{.4}\right)}{.4} ]
[ 152 = \left(4\times44\right)-4! ]
[ 153 = \frac{\left(44+4!\right)}{.\dot{4}} ]
[ 154 = 4+\frac{4!}{\left(.4\times.4\right)} ]
[ 155 = \frac{\left(\sqrt{4}+\frac{4!}{.4}\right)}{.4} ]
[ 156 = \frac{4!}{.4}+\left(4!\times4\right) ]
[ 158 = \frac{{\sqrt{\sqrt{\sqrt{4}}}}^{4!}}{.4}-\sqrt{4} ]
[ 159 = 4!+\frac{4!}{\left(.\dot{4}\times.4\right)} ]
[ 160 = \left(44-4\right)\times4 ]
[ 161 = \frac{\left({\sqrt{\sqrt{\sqrt{4}}}}^{4!}+.4\right)}{.4} ]
[ 162 = \sqrt{\left(4\times{\frac{4}{.\dot{4}}}^{4}\right)} ]
[ 164 = \frac{{\sqrt{\sqrt{\sqrt{4}}}}^{4!}}{.4}+4 ]
[ 165 = \frac{44}{\left(.4\times\sqrt{.\dot{4}}\right)} ]
[ 166 = {\left(4!+\sqrt{\sqrt{4!}}\right)}^{\sqrt{\sqrt{\left(4+\sqrt{4}\right)}}} ]
[ 168 = \left(44-\sqrt{4}\right)\times4 ]
[ 169 = \sqrt{{\left(\frac{4}{.\dot{4}}+4\right)}^{4}} ]
[ 170 = \frac{\left(44+4!\right)}{.4} ]
[ 172 = \left(4\times44\right)-4 ]
[ 174 = \left(4\times44\right)-\sqrt{4} ]
[ 175 = \frac{\left(4!+4\right)}{\left(.4\times.4\right)} ]
[ 176 = 44\times\sqrt{\left(4\times4\right)} ]
[ 178 = \left(4\times44\right)+\sqrt{4} ]
[ 180 = \left(4\times44\right)+4 ]
[ 181 = {4}^{\sqrt{\sqrt{\sqrt{{\sqrt{\sqrt{\sqrt{\left(4!\times\sqrt{\sqrt{4}}\right)}}}}^{4!}}}}} ]
[ 184 = 4\times\left(\sqrt{4}+44\right) ]
[ 188 = \left(\left(4+4\right)\times4!\right)-4 ]
[ 189 = \frac{\left(4!+\frac{4!}{.4}\right)}{.\dot{4}} ]
[ 190 = \left(\left(4+4\right)\times4!\right)-\sqrt{4} ]
[ 192 = \left(44+4\right)\times4 ]
[ 194 = \left(\left(4+4\right)\times4!\right)+\sqrt{4} ]
[ 195 = \frac{\left(4!+\frac{4!}{.\dot{4}}\right)}{.4} ]
[ 196 = 4+\left(\left(4+4\right)\times4!\right) ]
[ 198 = \frac{\left(44\times\sqrt{4}\right)}{.\dot{4}} ]
[ 200 = \left(4\times44\right)+4! ]
[ 202 = {4}^{4}-\frac{4!}{.\dot{4}} ]
[ 204 = 4!\times\left(\frac{\sqrt{4}}{.\dot{4}}+4\right) ]
[ 207 = \frac{\left(\left(4!\times4\right)-4\right)}{.\dot{4}} ]
[ 208 = \left(\left(4!\times\sqrt{4}\right)+4\right)\times4 ]
[ 210 = \frac{4}{.\dot{4}}\times\left(4!-\sqrt{.\dot{4}}\right) ]
[ 212 = {4}^{4}-44 ]
[ 214 = \frac{\left(4!\times4\right)}{.\dot{4}}-\sqrt{4} ]
[ 215 = \frac{\left(\left(4!\times4\right)-.\dot{4}\right)}{.\dot{4}} ]
[ 216 = \frac{\left(\left(4-.4\right)\times4!\right)}{.4} ]
[ 217 = \frac{\left(.\dot{4}+\left(4!\times4\right)\right)}{.\dot{4}} ]
[ 218 = \sqrt{4}+\frac{\left(4!\times4\right)}{.\dot{4}} ]
[ 220 = \frac{44}{.4}\times\sqrt{4} ]
[ 222 = \frac{444}{\sqrt{4}} ]
[ 224 = \left(4!+4\right)\times\left(4+4\right) ]
[ 225 = \frac{4}{\left(\left(.\dot{4}-.4\right)\times.4\right)} ]
[ 228 = {4}^{4}-\left(4!+4\right) ]
[ 230 = \frac{\left(\left(4!\times4\right)-4\right)}{.4} ]
[ 232 = \left(4+\frac{4!}{.\dot{4}}\right)\times4 ]
[ 234 = \frac{\left(\left(\sqrt{4}+4!\right)\times4\right)}{.\dot{4}} ]
[ 235 = \frac{\left(\left(4!\times4\right)-\sqrt{4}\right)}{.4} ]
[ 236 = \left(4-4!\right)+{4}^{4} ]
[ 238 = \left(\frac{4}{.4}\times4!\right)-\sqrt{4} ]
[ 239 = \frac{\left(\left(4!\times4\right)-.4\right)}{.4} ]
[ 240 = {4}^{4}-\left(4\times4\right) ]
[ 241 = \frac{\left(.4+\left(4!\times4\right)\right)}{.4} ]
[ 242 = \sqrt{4}+\left(\frac{4}{.4}\times4!\right) ]
[ 243 = \frac{\sqrt{4}}{\left(.\dot{4}\times.\dot{4}\right)}\times4! ]
[ 244 = \left(\frac{4}{.4}\times4!\right)+4 ]
[ 245 = \frac{\left(\left(4!\times4\right)+\sqrt{4}\right)}{.4} ]
[ 246 = {4}^{4}-\frac{4}{.4} ]
[ 247 = {4}^{4}-\frac{4}{.\dot{4}} ]
[ 248 = \left({4}^{4}-4\right)-4 ]
[ 250 = {4}^{4}-\left(4+\sqrt{4}\right) ]
[ 251 = {4}^{4}-\frac{\sqrt{4}}{.4} ]
[ 252 = \frac{\left(\left(4!+4\right)\times4\right)}{.\dot{4}} ]
[ 253 = {4}^{4}-\sqrt{\frac{4}{.\dot{4}}} ]
[ 254 = \left({4}^{4}-4\right)+\sqrt{4} ]
[ 255 = {4}^{4}-\frac{4}{4} ]
[ 256 = \left(4\times\left(4\times4\right)\right)\times4 ]
[ 257 = {4}^{4}+\frac{4}{4} ]
[ 258 = 4+\left({4}^{4}-\sqrt{4}\right) ]
[ 259 = \sqrt{\frac{4}{.\dot{4}}}+{4}^{4} ]
[ 260 = {4}^{4}+\sqrt{\left(4\times4\right)} ]
[ 261 = \frac{\sqrt{4}}{.4}+{4}^{4} ]
[ 262 = {4}^{4}+\left(4+\sqrt{4}\right) ]
[ 264 = 44\times\left(4+\sqrt{4}\right) ]
[ 265 = \frac{4}{.\dot{4}}+{4}^{4} ]
[ 266 = \frac{4}{.4}+{4}^{4} ]
[ 268 = {4}^{4}+\frac{4!}{\sqrt{4}} ]
[ 270 = \frac{\left(4!+\left(4!\times4\right)\right)}{.\dot{4}} ]
[ 272 = 4\times\left(44+4!\right) ]
[ 275 = \frac{44}{\left(.4\times.4\right)} ]
[ 276 = \left(4!-4\right)+{4}^{4} ]
[ 278 = \left({4}^{4}-\sqrt{4}\right)+4! ]
[ 280 = \frac{4}{.4}\times\left(4!+4\right) ]
[ 282 = \left({4}^{4}+4!\right)+\sqrt{4} ]
[ 284 = \left({4}^{4}+4\right)+4! ]
[ 286 = \frac{\left(\left(4!\times4!\right)-4\right)}{\sqrt{4}} ]
[ 287 = \frac{\left(\left(4!\times4!\right)-\sqrt{4}\right)}{\sqrt{4}} ]
[ 288 = \left(4+\left(4+4\right)\right)\times4! ]
[ 289 = \frac{\left(\left(4!\times4!\right)+\sqrt{4}\right)}{\sqrt{4}} ]
[ 290 = \frac{\left(\left(4!\times4!\right)+4\right)}{\sqrt{4}} ]
[ 292 = 4+\sqrt{\frac{{4!}^{4}}{4}} ]
[ 294 = \sqrt{{\left(\frac{\sqrt{4!}}{.4}+\sqrt{4!}\right)}^{4}} ]
[ 296 = 444\times\sqrt{.\dot{4}} ]
[ 300 = 44+{4}^{4} ]
[ 304 = \left({4}^{4}+4!\right)+4! ]
[ 310 = \frac{4!}{.\dot{4}}+{4}^{4} ]
[ 312 = 4!\times\left(\frac{4}{.\dot{4}}+4\right) ]
[ 316 = {4}^{4}+\frac{4!}{.4} ]
[ 320 = \left(4!-4\right)\times\left(4\times4\right) ]
[ 324 = \frac{{\left(4+\sqrt{4}\right)}^{4}}{4} ]
[ 336 = \left(\frac{4}{.4}+4\right)\times4! ]
[ 338 = \sqrt{\frac{{\left(\sqrt{4}+4!\right)}^{4}}{4}} ]
[ 343 = {\sqrt{\sqrt{\sqrt{\frac{\left(4!+4\right)}{4}}}}}^{4!} ]
[ 348 = \frac{\left({4}^{4}-4!\right)}{\sqrt{.\dot{4}}} ]
[ 351 = \frac{4!}{\sqrt{{\sqrt{\sqrt{.4}}}^{4!}}}-4! ]
[ 352 = \left(4+4\right)\times44 ]
[ 360 = \frac{\left(4\times4\right)}{\left(.\dot{4}-.4\right)} ]
[ 361 = \sqrt{{\left(4!-\frac{\sqrt{4}}{.4}\right)}^{4}} ]
[ 368 = \left(\left(4!\times4\right)-4\right)\times4 ]
[ 371 = \frac{4!}{\sqrt{{\sqrt{\sqrt{.4}}}^{4!}}}-4 ]
[ 373 = \frac{4!}{\sqrt{{\sqrt{\sqrt{.4}}}^{4!}}}-\sqrt{4} ]
[ 375 = \frac{4!}{\left(.4\times\left(.4\times.4\right)\right)} ]
[ 376 = 4\times\left(\left(4!\times4\right)-\sqrt{4}\right) ]
[ 377 = \sqrt{4}+\frac{4!}{\sqrt{{\sqrt{\sqrt{.4}}}^{4!}}} ]
[ 378 = \frac{\left({4}^{4}-4\right)}{\sqrt{.\dot{4}}} ]
[ 379 = 4+\frac{4!}{\sqrt{{\sqrt{\sqrt{.4}}}^{4!}}} ]
[ 380 = \left(4\times\left(4!\times4\right)\right)-4 ]
[ 381 = \frac{\left({4}^{4}-\sqrt{4}\right)}{\sqrt{.\dot{4}}} ]
[ 382 = \left(4\times\left(4!\times4\right)\right)-\sqrt{4} ]
[ 383 = \frac{\left({4}^{4}-\sqrt{.\dot{4}}\right)}{\sqrt{.\dot{4}}} ]
[ 384 = \left(\sqrt{\left(4\times4\right)}\times4\right)\times4! ]
[ 385 = \frac{\left({4}^{4}+\sqrt{.\dot{4}}\right)}{\sqrt{.\dot{4}}} ]
[ 386 = \sqrt{4}+\left(4\times\left(4!\times4\right)\right) ]
[ 387 = \frac{\left({4}^{4}+\sqrt{4}\right)}{\sqrt{.\dot{4}}} ]
[ 388 = 4+\left(4\times\left(4!\times4\right)\right) ]
[ 390 = \frac{\left({4}^{4}+4\right)}{\sqrt{.\dot{4}}} ]
[ 392 = 4\times\left(\left(4!\times4\right)+\sqrt{4}\right) ]
[ 396 = \frac{\left(4\times44\right)}{.\dot{4}} ]
[ 398 = {\sqrt{\left(4!-4\right)}}^{4}-\sqrt{4} ]
[ 399 = 4!+\frac{4!}{\sqrt{{\sqrt{\sqrt{.4}}}^{4!}}} ]
[ 400 = \left(4+\left(4!\times4\right)\right)\times4 ]
[ 402 = \sqrt{{\left(4!-4\right)}^{4}}+\sqrt{4} ]
[ 404 = 4+{\sqrt{\left(4!-4\right)}}^{4} ]
[ 408 = 4!+\left(4\times\left(4!\times4\right)\right) ]
[ 416 = \left(\left(\sqrt{4}+4!\right)\times4\right)\times4 ]
[ 420 = 444-4! ]
[ 424 = {\sqrt{\left(4!-4\right)}}^{4}+4! ]
[ 432 = \frac{\left(4+4\right)}{.\dot{4}}\times4! ]
[ 440 = 444-4 ]
[ 441 = \sqrt{{\left(4!-\sqrt{\frac{4}{.\dot{4}}}\right)}^{4}} ]
[ 442 = 444-\sqrt{4} ]
[ 444 = {\sqrt{444}}^{\sqrt{4}} ]
[ 446 = \sqrt{4}+444 ]
[ 448 = 4+444 ]
[ 450 = \frac{\left(4!-4\right)}{\left(.\dot{4}-.4\right)} ]
[ 456 = \left(4!\times\left(4!-4\right)\right)-4! ]
[ 460 = {\sqrt{\left(4!-\sqrt{4}\right)}}^{4}-4! ]
[ 464 = \left({4}^{4}-4!\right)\times\sqrt{4} ]
[ 468 = 444+4! ]
[ 472 = \left(.4-4!\right)\times\left(4-4!\right) ]
[ 476 = \left(4!\times\left(4!-4\right)\right)-4 ]
[ 478 = \left(4!\times\left(4!-4\right)\right)-\sqrt{4} ]
[ 480 = 4!\times\left(4+\left(4\times4\right)\right) ]
[ 482 = \left(4!\times\left(4!-4\right)\right)+\sqrt{4} ]
[ 484 = \frac{{\sqrt{44}}^{4}}{4} ]
[ 486 = \frac{4!}{\left(.\dot{4}\times.\dot{4}\right)}\times4 ]
[ 488 = \left(4!+.4\right)\times\left(4!-4\right) ]
[ 495 = \frac{\left(\sqrt{4}-4!\right)}{\left(.4-.\dot{4}\right)} ]
[ 496 = \left(\left(\sqrt{.\dot{4}}-4\right)+4!\right)\times4! ]
[ 500 = \sqrt{\frac{{\sqrt{\sqrt{\frac{4}{.4}}}}^{4!}}{4}} ]
[ 504 = \left({4}^{4}-4\right)\times\sqrt{4} ]
[ 508 = \left({4}^{4}\times\sqrt{4}\right)-4 ]
[ 510 = \left({4}^{4}\times\sqrt{4}\right)-\sqrt{4} ]
[ 512 = {4}^{4}+{4}^{4} ]
[ 514 = \sqrt{4}+\left({4}^{4}\times\sqrt{4}\right) ]
[ 516 = \left({4}^{4}\times\sqrt{4}\right)+4 ]
[ 520 = \left({4}^{4}+4\right)\times\sqrt{4} ]
[ 522 = \frac{\left({4}^{4}-4!\right)}{.\dot{4}} ]
[ 524 = \left(4!\times\left(4!-\sqrt{4}\right)\right)-4 ]
[ 525 = \frac{\left(\sqrt{.\dot{4}}-4!\right)}{\left(.4-.\dot{4}\right)} ]
[ 526 = \left(4!\times\left(4!-\sqrt{4}\right)\right)-\sqrt{4} ]
[ 528 = \frac{44}{\sqrt{4}}\times4! ]
[ 529 = \sqrt{{\left(4!-\frac{4}{4}\right)}^{4}} ]
[ 530 = \frac{\left(.\dot{4}-4!\right)}{\left(.4-.\dot{4}\right)} ]
[ 531 = \frac{\left(4!-.4\right)}{\left(.\dot{4}-.4\right)} ]
[ 532 = \left(4!\times4!\right)-44 ]
[ 536 = \frac{4!}{\left(.\dot{4}-.4\right)}-4 ]
[ 538 = \frac{4!}{\left(.\dot{4}-.4\right)}-\sqrt{4} ]
[ 540 = \frac{4}{\left(.\dot{4}\times.4\right)}\times4! ]
[ 542 = \sqrt{4}+\frac{4!}{\left(.\dot{4}-.4\right)} ]
[ 544 = 4-\frac{4!}{\left(.4-.\dot{4}\right)} ]
[ 548 = \left(\left(4!\times4!\right)-4\right)-4! ]
[ 549 = \frac{\left(4!+.4\right)}{\left(.\dot{4}-.4\right)} ]
[ 550 = \frac{\left(4!+.\dot{4}\right)}{\left(.\dot{4}-.4\right)} ]
[ 552 = \frac{{4}^{4}}{.\dot{4}}-4! ]
[ 554 = \left(\left(4!\times4!\right)-4!\right)+\sqrt{4} ]
[ 555 = \frac{\left(4!+\sqrt{.\dot{4}}\right)}{\left(.\dot{4}-.4\right)} ]
[ 556 = \left(\left(4!\times4!\right)+4\right)-4! ]
[ 558 = \left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right)-\sqrt{4} ]
[ 560 = \left(4!-4\right)\times\left(4!+4\right) ]
[ 562 = \sqrt{4}+\left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right) ]
[ 564 = \frac{4!}{\left(.\dot{4}-.4\right)}+4! ]
[ 566 = \left(4!\times4!\right)-\frac{4}{.4} ]
[ 567 = \frac{\left({4}^{4}-4\right)}{.\dot{4}} ]
[ 568 = \left(4!\times4!\right)-\left(4+4\right) ]
[ 570 = \left(4!\times4!\right)-\left(4+\sqrt{4}\right) ]
[ 571 = \left(4!\times4!\right)-\frac{\sqrt{4}}{.4} ]
[ 572 = \frac{{4}^{4}}{.\dot{4}}-4 ]
[ 573 = \left(4!\times4!\right)-\sqrt{\frac{4}{.\dot{4}}} ]
[ 574 = \frac{{4}^{4}}{.\dot{4}}-\sqrt{4} ]
[ 575 = \frac{\left({4}^{4}-.\dot{4}\right)}{.\dot{4}} ]
[ 576 = {\left(4+\sqrt{4}\right)}^{4}\times.\dot{4} ]
[ 577 = \frac{\left(.\dot{4}+{4}^{4}\right)}{.\dot{4}} ]
[ 578 = \frac{{4}^{4}}{.\dot{4}}+\sqrt{4} ]
[ 579 = \left(4!\times4!\right)+\sqrt{\frac{4}{.\dot{4}}} ]
[ 580 = \frac{{4}^{4}}{.\dot{4}}+4 ]
[ 581 = \frac{\sqrt{4}}{.4}+\left(4!\times4!\right) ]
[ 582 = \left(\left(4!\times4!\right)+\sqrt{4}\right)+4 ]
[ 584 = 4+\left(\left(4!\times4!\right)+4\right) ]
[ 585 = \frac{\left({4}^{4}+4\right)}{.\dot{4}} ]
[ 586 = \frac{4}{.4}+\left(4!\times4!\right) ]
[ 588 = \left(4!+\frac{\sqrt{4}}{4}\right)\times4! ]
[ 590 = \left(4!\times\left(4!+\sqrt{.\dot{4}}\right)\right)-\sqrt{4} ]
[ 592 = \left(4!\times4!\right)+\left(4\times4\right) ]
[ 594 = \left(4!\times\left(4!+\sqrt{.\dot{4}}\right)\right)+\sqrt{4} ]
[ 596 = \left(4!+\left(4!\times4!\right)\right)-4 ]
[ 598 = \left(4!-\sqrt{4}\right)+\left(4!\times4!\right) ]
[ 600 = \frac{\left(4!\times4\right)}{\left(.4\times.4\right)} ]
[ 601 = {\frac{\sqrt{4}}{.4}}^{4}-4! ]
[ 602 = \left(4!+\left(4!\times4!\right)\right)+\sqrt{4} ]
[ 604 = \left(4!\times4!\right)+\left(4!+4\right) ]
[ 608 = 4!\times\left(4!+\sqrt{\left(4\times.\dot{4}\right)}\right) ]
[ 612 = 4!\times\left(\frac{\sqrt{.\dot{4}}}{.\dot{4}}+4!\right) ]
[ 616 = \frac{{4}^{4}}{.4}-4! ]
[ 620 = \left(4!\times4!\right)+44 ]
[ 621 = {\frac{\sqrt{4}}{.4}}^{4}-4 ]
[ 622 = \left(4!\times\left(\sqrt{4}+4!\right)\right)-\sqrt{4} ]
[ 623 = {\frac{\sqrt{4}}{.4}}^{4}-\sqrt{4} ]
[ 624 = \left(\left(4-\sqrt{4}\right)+4!\right)\times4! ]
[ 625 = {\left(\frac{4}{4}+4\right)}^{4} ]
[ 626 = \sqrt{4}+\left(4!\times\left(\sqrt{4}+4!\right)\right) ]
[ 627 = \sqrt{4}+{\frac{\sqrt{4}}{.4}}^{4} ]
[ 628 = 4+\left(4!\times\left(\sqrt{4}+4!\right)\right) ]
[ 629 = {\frac{\sqrt{4}}{.4}}^{4}+4 ]
[ 630 = \frac{\left({4}^{4}-4\right)}{.4} ]
[ 635 = \frac{\left({4}^{4}-\sqrt{4}\right)}{.4} ]
[ 636 = \frac{{4}^{4}}{.4}-4 ]
[ 638 = \frac{{4}^{4}}{.4}-\sqrt{4} ]
[ 639 = \frac{\left({4}^{4}-.4\right)}{.4} ]
[ 640 = \frac{\sqrt{{\left(4\times4\right)}^{4}}}{.4} ]
[ 641 = \frac{\left({4}^{4}+.4\right)}{.4} ]
[ 642 = \sqrt{4}+\frac{{4}^{4}}{.4} ]
[ 644 = 4+\frac{{4}^{4}}{.4} ]
[ 645 = \frac{\left({4}^{4}+\sqrt{4}\right)}{.4} ]
[ 648 = \frac{\left(4!\times4!\right)}{\left(.\dot{4}+.\dot{4}\right)} ]
[ 649 = {\frac{\sqrt{4}}{.4}}^{4}+4! ]
[ 650 = \frac{\left({4}^{4}+4\right)}{.4} ]
[ 652 = {\sqrt{\left(\sqrt{4}+4!\right)}}^{4}-4! ]
[ 656 = \left(\left(4!+4\right)-\sqrt{.\dot{4}}\right)\times4! ]
[ 664 = \frac{{4}^{4}}{.4}+4! ]
[ 666 = \frac{444}{\sqrt{.\dot{4}}} ]
[ 668 = \left(\left(4!+4\right)\times4!\right)-4 ]
[ 670 = \left(\left(4!+4\right)\times4!\right)-\sqrt{4} ]
[ 672 = \left(4!+\sqrt{\left(4\times4\right)}\right)\times4! ]
[ 674 = \sqrt{4}+\left(\left(4!+4\right)\times4!\right) ]
[ 676 = 4+\left(\left(4!+4\right)\times4!\right) ]
[ 678 = \sqrt{4}+\sqrt{{\left(\sqrt{4}+4!\right)}^{4}} ]
[ 680 = 4+{\sqrt{\left(\sqrt{4}+4!\right)}}^{4} ]
[ 684 = \left(4!+\frac{\sqrt{4}}{.\dot{4}}\right)\times4! ]
[ 688 = 4!\times\left(\left(4!+4\right)+\sqrt{.\dot{4}}\right) ]
[ 696 = 4!+\left(\left(4!+4\right)\times4!\right) ]
[ 700 = \frac{\left({4}^{4}+4!\right)}{.4} ]
[ 704 = 44\times\left(4\times4\right) ]
[ 705 = {\sqrt{\sqrt{\sqrt{\frac{4}{.\dot{4}}}}}}^{4!}-4! ]
[ 720 = \frac{4!}{\left(.4+.4\right)}\times4! ]
[ 725 = \sqrt{{\sqrt{\sqrt{\frac{4}{.\dot{4}}}}}^{4!}}-4 ]
[ 726 = \sqrt{\frac{{\left(4!-\sqrt{4}\right)}^{4}}{.\dot{4}}} ]
[ 727 = \sqrt{{\sqrt{\sqrt{\frac{4}{.\dot{4}}}}}^{4!}}-\sqrt{4} ]
[ 728 = \left(\sqrt{4}+4!\right)\times\left(4!+4\right) ]
[ 729 = {\frac{4}{.\dot{4}}}^{\sqrt{\frac{4}{.\dot{4}}}} ]
[ 731 = {\sqrt{\sqrt{\sqrt{\frac{4}{.\dot{4}}}}}}^{4!}+\sqrt{4} ]
[ 733 = \sqrt{{\sqrt{\sqrt{\frac{4}{.\dot{4}}}}}^{4!}}+4 ]
[ 750 = 4!\times\sqrt{\frac{4}{\sqrt{{\sqrt{.4}}^{4!}}}} ]
[ 753 = \sqrt{{\sqrt{\sqrt{\frac{4}{.\dot{4}}}}}^{4!}}+4! ]
[ 760 = {\left(4!+4\right)}^{\sqrt{4}}-4! ]
[ 768 = \left(\left(4+4\right)\times4\right)\times4! ]
[ 780 = {\left(4!+4\right)}^{\sqrt{4}}-4 ]
[ 782 = {\left(4!+4\right)}^{\sqrt{4}}-\sqrt{4} ]
[ 784 = \left(4!+4\right)\times\left(4!+4\right) ]
[ 786 = \sqrt{4}+\sqrt{{\left(4!+4\right)}^{4}} ]
[ 788 = \sqrt{{\left(4!+4\right)}^{4}}+4 ]
[ 792 = 4!\times\left(\frac{4}{.\dot{4}}+4!\right) ]
[ 800 = \sqrt{\left(4\times{\left(4!-4\right)}^{4}\right)} ]
[ 808 = {\left(4!+4\right)}^{\sqrt{4}}+4! ]
[ 810 = \frac{4!}{\left(\sqrt{.\dot{4}}\times\left(.\dot{4}-.4\right)\right)} ]
[ 816 = \left(4!+\frac{4}{.4}\right)\times4! ]
[ 828 = \frac{\left(\left(4!\times4!\right)-4!\right)}{\sqrt{.\dot{4}}} ]
[ 832 = {4}^{4}+\left(4!\times4!\right) ]
[ 840 = \sqrt{\frac{{4!}^{4}}{.\dot{4}}}-4! ]
[ 841 = \sqrt{{\left(4!+\frac{\sqrt{4}}{.4}\right)}^{4}} ]
[ 848 = \left(4!-.\dot{4}\right)\times\frac{4!}{\sqrt{.\dot{4}}} ]
[ 858 = \frac{\left(\left(4!\times4!\right)-4\right)}{\sqrt{.\dot{4}}} ]
[ 860 = \sqrt{\frac{{4!}^{4}}{.\dot{4}}}-4 ]
[ 861 = \frac{\left(\left(4!\times4!\right)-\sqrt{4}\right)}{\sqrt{.\dot{4}}} ]
[ 862 = \sqrt{\frac{{4!}^{4}}{.\dot{4}}}-\sqrt{4} ]
[ 863 = \frac{\left(\left(4!\times4!\right)-\sqrt{.\dot{4}}\right)}{\sqrt{.\dot{4}}} ]
[ 864 = \frac{\left(4!\times4\right)}{.\dot{4}}\times4 ]
[ 865 = \frac{\left(\sqrt{.\dot{4}}+\left(4!\times4!\right)\right)}{\sqrt{.\dot{4}}} ]
[ 866 = \sqrt{\frac{{4!}^{4}}{.\dot{4}}}+\sqrt{4} ]
[ 867 = \frac{\left(\left(4!\times4!\right)+\sqrt{4}\right)}{\sqrt{.\dot{4}}} ]
[ 868 = 4+\sqrt{\frac{{4!}^{4}}{.\dot{4}}} ]
[ 870 = \frac{\left(\left(4!\times4!\right)+4\right)}{\sqrt{.\dot{4}}} ]
[ 880 = 44\times\left(4!-4\right) ]
[ 887 = {4}^{\sqrt{4!}}-\left(4-\sqrt{\sqrt{.\dot{4}}}\right) ]
[ 888 = \sqrt{4}\times444 ]
[ 889 = \left({4}^{\sqrt{4!}}-\sqrt{4}\right)+\sqrt{\sqrt{.\dot{4}}} ]
[ 891 = \frac{4}{\sqrt{4!}}+{4}^{\sqrt{4!}} ]
[ 893 = \left(\sqrt{4}+{4}^{\sqrt{4!}}\right)+\sqrt{\sqrt{.\dot{4}}} ]
[ 895 = \left(\sqrt{\sqrt{.\dot{4}}}+{4}^{\sqrt{4!}}\right)+4 ]
[ 896 = \left(\sqrt{4}-.\dot{4}\right)\times\left(4!\times4!\right) ]
[ 900 = \frac{\sqrt{{\left(4!-4\right)}^{4}}}{.\dot{4}} ]
[ 912 = \left(\frac{4!}{\sqrt{.\dot{4}}}+\sqrt{4}\right)\times4! ]
[ 915 = 4!+\left(\sqrt{\sqrt{.\dot{4}}}+{4}^{\sqrt{4!}}\right) ]
[ 928 = 4\times\left({4}^{4}-4!\right) ]
[ 936 = \left(\sqrt{4}+4!\right)\times\frac{4!}{\sqrt{.\dot{4}}} ]
[ 960 = 4!\times\left(44-4\right) ]
[ 968 = 44\times\left(4!-\sqrt{4}\right) ]
[ 976 = {\sqrt{\sqrt{\sqrt{\frac{4}{.4}}}}}^{4!}-4! ]
[ 990 = \frac{44}{\left(.\dot{4}-.4\right)} ]
[ 996 = \sqrt{{\sqrt{\sqrt{\frac{4}{.4}}}}^{4!}}-4 ]
[ 998 = \sqrt{{\sqrt{\sqrt{\frac{4}{.4}}}}^{4!}}-\sqrt{4} ]
[ 999 = \frac{444}{.\dot{4}} ]
[ 1000 = \left({4}^{4}\times4\right)-4! ]
[ 1002 = \sqrt{4}+\sqrt{{\sqrt{\sqrt{\frac{4}{.4}}}}^{4!}} ]
[ 1004 = \sqrt{{\sqrt{\sqrt{\frac{4}{.4}}}}^{4!}}+4 ]
[ 1008 = 4\times\left({4}^{4}-4\right) ]
[ 1014 = \frac{\sqrt{{\left(\sqrt{4}+4!\right)}^{4}}}{\sqrt{.\dot{4}}} ]
[ 1016 = \left({4}^{4}-\sqrt{4}\right)\times4 ]
[ 1018 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4!\right)}{4} ]
[ 1020 = \left({4}^{4}\times4\right)-4 ]
[ 1022 = \left({4}^{4}\times4\right)-\sqrt{4} ]
[ 1023 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4\right)}{4} ]
[ 1024 = {4}^{\left(\frac{4}{4}+4\right)} ]
[ 1025 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}+4\right)}{4} ]
[ 1026 = \sqrt{4}+\left({4}^{4}\times4\right) ]
[ 1028 = \left({4}^{4}\times4\right)+4 ]
[ 1030 = \frac{\left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)}{4} ]
[ 1032 = \left(44\times4!\right)-4! ]
[ 1040 = 4\times\left({4}^{4}+4\right) ]
[ 1048 = \left({4}^{4}\times4\right)+4! ]
[ 1052 = \left(44\times4!\right)-4 ]
[ 1054 = \left(44\times4!\right)-\sqrt{4} ]
[ 1056 = \sqrt{\left(4\times4\right)}!\times44 ]
[ 1058 = \left(44\times4!\right)+\sqrt{4} ]
[ 1060 = \left(44\times4!\right)+4 ]
[ 1072 = \left(44+\sqrt{.\dot{4}}\right)\times4! ]
[ 1080 = \left(44\times4!\right)+4! ]
[ 1089 = {\sqrt{\left(\frac{4}{.\dot{4}}+4!\right)}}^{4} ]
[ 1104 = \left(\sqrt{4}+44\right)\times4! ]
[ 1110 = \frac{444}{.4} ]
[ 1120 = \left({4}^{4}+4!\right)\times4 ]
[ 1128 = \left(\left(4!\times\sqrt{4}\right)\times4!\right)-4! ]
[ 1136 = 4!\times\left(\left(4!\times\sqrt{4}\right)-\sqrt{.\dot{4}}\right) ]
[ 1144 = 44\times\left(\sqrt{4}+4!\right) ]
[ 1148 = \left(\left(4!\times\sqrt{4}\right)\times4!\right)-4 ]
[ 1150 = \left(\left(4!\times\sqrt{4}\right)\times4!\right)-\sqrt{4} ]
[ 1152 = 4!\times\left(44+4\right) ]
[ 1154 = \left(\left(4!\times\sqrt{4}\right)\times4!\right)+\sqrt{4} ]
[ 1156 = 4+\left(\left(4!\times\sqrt{4}\right)\times4!\right) ]
[ 1160 = \sqrt{4}\times\left(\left(4!\times4!\right)+4\right) ]
[ 1168 = 4!\times\left(\sqrt{.\dot{4}}+\left(4!\times\sqrt{4}\right)\right) ]
[ 1176 = \frac{\sqrt{{\left(4!+4\right)}^{4}}}{\sqrt{.\dot{4}}} ]
[ 1184 = \left(4!\times\left(4!+\sqrt{.\dot{4}}\right)\right)\times\sqrt{4} ]
[ 1188 = \frac{\left(4!-\sqrt{4}\right)}{.\dot{4}}\times4! ]
[ 1200 = \frac{\left(4!-4\right)}{.4}\times4! ]
[ 1210 = \frac{\sqrt{{\left(4!-\sqrt{4}\right)}^{4}}}{.4} ]
[ 1215 = \frac{4!}{\left(\left(.\dot{4}-.4\right)\times.\dot{4}\right)} ]
[ 1225 = \frac{\sqrt{{\left(4!-\sqrt{.\dot{4}}\right)}^{4}}}{.\dot{4}} ]
[ 1232 = 44\times\left(4!+4\right) ]
[ 1242 = \frac{\left(\left(4!\times4!\right)-4!\right)}{.\dot{4}} ]
[ 1248 = 4!\times\left(\left(4!\times\sqrt{4}\right)+4\right) ]
[ 1250 = {\frac{\sqrt{4}}{.4}}^{4}\times\sqrt{4} ]
[ 1260 = 4!\times\frac{\left(4!-\sqrt{.\dot{4}}\right)}{.\dot{4}} ]
[ 1272 = {\left(4+\sqrt{4}\right)}^{4}-4! ]
[ 1280 = \frac{\left({4}^{4}\times\sqrt{4}\right)}{.4} ]
[ 1287 = \frac{\left(\left(4!\times4!\right)-4\right)}{.\dot{4}} ]
[ 1292 = {\left(4+\sqrt{4}\right)}^{4}-4 ]
[ 1294 = {\left(4+\sqrt{4}\right)}^{4}-\sqrt{4} ]
[ 1295 = \frac{\left(\left(4!\times4!\right)-.\dot{4}\right)}{.\dot{4}} ]
[ 1296 = {\left(\frac{4}{.4}-4\right)}^{4} ]
[ 1297 = \frac{\left(.\dot{4}+\left(4!\times4!\right)\right)}{.\dot{4}} ]
[ 1298 = \sqrt{4}+{\left(4+\sqrt{4}\right)}^{4} ]
[ 1300 = {\left(4+\sqrt{4}\right)}^{4}+4 ]
[ 1305 = \frac{\left(\left(4!\times4!\right)+4\right)}{.\dot{4}} ]
[ 1312 = 4!\times\left(\sqrt{.\dot{4}}+\frac{4!}{.\dot{4}}\right) ]
[ 1320 = {\left(4+\sqrt{4}\right)}^{4}+4! ]
[ 1331 = {\sqrt{\sqrt{\sqrt{\frac{44}{4}}}}}^{4!} ]
[ 1332 = \frac{\left(4!\times\left(4!+\sqrt{.\dot{4}}\right)\right)}{.\dot{4}} ]
[ 1344 = 4!\times\left(\frac{4!}{.4}-4\right) ]
[ 1350 = \frac{4!}{\left(\left(.\dot{4}-.4\right)\times.4\right)} ]
[ 1352 = \sqrt{4}\times\sqrt{{\left(\sqrt{4}+4!\right)}^{4}} ]
[ 1369 = \frac{{\sqrt{\left(4!+\sqrt{.\dot{4}}\right)}}^{4}}{.\dot{4}} ]
[ 1380 = \frac{\left(\left(4!\times4!\right)-4!\right)}{.4} ]
[ 1392 = 4!\times\left(4+\frac{4!}{.\dot{4}}\right) ]
[ 1400 = \frac{\left(4!-\sqrt{.\dot{4}}\right)}{.4}\times4! ]
[ 1404 = 4!\times\frac{\left(\sqrt{4}+4!\right)}{.\dot{4}} ]
[ 1408 = \left(.\dot{4}+\sqrt{4}\right)\times\left(4!\times4!\right) ]
[ 1416 = \frac{\left(4!-.4\right)}{.4}\times4! ]
[ 1424 = 4!\times\left(\frac{4!}{.4}-\sqrt{.\dot{4}}\right) ]
[ 1430 = \frac{\left(\left(4!\times4!\right)-4\right)}{.4} ]
[ 1435 = \frac{\left(\left(4!\times4!\right)-\sqrt{4}\right)}{.4} ]
[ 1436 = \left(4!\times\frac{4!}{.4}\right)-4 ]
[ 1438 = \left(4!\times\frac{4!}{.4}\right)-\sqrt{4} ]
[ 1439 = \frac{\left(\left(4!\times4!\right)-.4\right)}{.4} ]
[ 1440 = \frac{{4}^{4}}{\left(.\dot{4}\times.4\right)} ]
[ 1441 = \frac{\left(.4+\left(4!\times4!\right)\right)}{.4} ]
[ 1442 = \left(4!\times\frac{4!}{.4}\right)+\sqrt{4} ]
[ 1444 = \left(4!\times\frac{4!}{.4}\right)+4 ]
[ 1445 = \frac{\left(\left(4!\times4!\right)+\sqrt{4}\right)}{.4} ]
[ 1450 = \frac{\left(\left(4!\times4!\right)+4\right)}{.4} ]
[ 1456 = \left(\frac{4!}{.4}+\sqrt{.\dot{4}}\right)\times4! ]
[ 1458 = \frac{{\sqrt{\frac{4!}{.\dot{4}}}}^{4}}{\sqrt{4}} ]
[ 1464 = 4!\times\frac{\left(4!+.4\right)}{.4} ]
[ 1480 = \frac{\left(4!+\sqrt{.\dot{4}}\right)}{.4}\times4! ]
[ 1488 = \left(\sqrt{4}+\frac{4!}{.4}\right)\times4! ]
[ 1500 = \frac{\left(4!+\left(4!\times4!\right)\right)}{.4} ]
[ 1512 = \frac{\left(4!+4\right)}{.\dot{4}}\times4! ]
[ 1520 = 4!\times\left({\sqrt{\sqrt{\sqrt{4}}}}^{4!}-\sqrt{.\dot{4}}\right) ]
[ 1521 = \frac{{\sqrt{\left(\sqrt{4}+4!\right)}}^{4}}{.\dot{4}} ]
[ 1532 = \left(\sqrt{{\sqrt{\sqrt{4}}}^{4!}}\times4!\right)-4 ]
[ 1534 = \left(\sqrt{{\sqrt{\sqrt{4}}}^{4!}}\times4!\right)-\sqrt{4} ]
[ 1536 = \left(4\times\left(4!\times4\right)\right)\times4 ]
[ 1538 = \left(\sqrt{{\sqrt{\sqrt{4}}}^{4!}}\times4!\right)+\sqrt{4} ]
[ 1540 = \left(\sqrt{{\sqrt{\sqrt{4}}}^{4!}}\times4!\right)+4 ]
[ 1552 = 4!\times\left(\sqrt{{\sqrt{\sqrt{4}}}^{4!}}+\sqrt{.\dot{4}}\right) ]
[ 1560 = \frac{\left(\sqrt{4}+4!\right)}{.4}\times4! ]
[ 1568 = \sqrt{{\left(4!+4\right)}^{4}}\times\sqrt{4} ]
[ 1576 = {\frac{4}{\sqrt{.4}}}^{4}-4! ]
[ 1584 = \frac{\left(44\times4!\right)}{\sqrt{.\dot{4}}} ]
[ 1596 = {\frac{4}{\sqrt{.4}}}^{4}-4 ]
[ 1598 = {\frac{4}{\sqrt{.4}}}^{4}-\sqrt{4} ]
[ 1600 = {\left(44-4\right)}^{\sqrt{4}} ]
[ 1602 = {\frac{4}{\sqrt{.4}}}^{4}+\sqrt{4} ]
[ 1604 = 4+{\frac{4}{\sqrt{.4}}}^{4} ]
[ 1624 = 4!+{\frac{4}{\sqrt{.4}}}^{4} ]
[ 1632 = 4!\times\left(44+4!\right) ]
[ 1638 = \left(.4\times{\sqrt{\sqrt{4}}}^{4!}\right)-.4 ]
[ 1640 = \left({\sqrt{\sqrt{4}}}^{4!}+4\right)\times.4 ]
[ 1648 = \left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)\times.4 ]
[ 1664 = {\sqrt{\sqrt{\sqrt{4}}}}^{4!}\times\left(\sqrt{4}+4!\right) ]
[ 1680 = \frac{\left(\left(4!+4\right)\times4!\right)}{.4} ]
[ 1690 = \frac{{\sqrt{\left(\sqrt{4}+4!\right)}}^{4}}{.4} ]
[ 1704 = {\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{4}}}}}}^{4!}-4! ]
[ 1724 = {\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{4}}}}}}^{4!}-4 ]
[ 1726 = {\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{4}}}}}}^{4!}-\sqrt{4} ]
[ 1728 = \left(\left(4!\times4\right)-4!\right)\times4! ]
[ 1730 = \sqrt{4}+{\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{4}}}}}}^{4!} ]
[ 1732 = {\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{4}}}}}}^{4!}+4 ]
[ 1752 = 4!+{\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{4}}}}}}^{4!} ]
[ 1764 = {\sqrt{\left(44-\sqrt{4}\right)}}^{4} ]
[ 1776 = 444\times4 ]
[ 1792 = \left(4!+4\right)\times\sqrt{{\sqrt{\sqrt{4}}}^{4!}} ]
[ 1800 = \frac{{\sqrt{\frac{4!}{.4}}}^{4}}{\sqrt{4}} ]
[ 1820 = \left({\sqrt{\sqrt{4}}}^{4!}\times.\dot{4}\right)-.\dot{4} ]
[ 1872 = 4!\times\left(4!+\frac{4!}{.\dot{4}}\right) ]
[ 1875 = \frac{4!}{{.4}^{4}}\times\sqrt{4} ]
[ 1912 = {\sqrt{44}}^{4}-4! ]
[ 1920 = \left(4!\times\left(4!-4\right)\right)\times4 ]
[ 1932 = {\sqrt{44}}^{4}-4 ]
[ 1934 = {\sqrt{44}}^{4}-\sqrt{4} ]
[ 1936 = 44\times44 ]
[ 1938 = {\sqrt{44}}^{4}+\sqrt{4} ]
[ 1940 = {\sqrt{44}}^{4}+4 ]
[ 1944 = \sqrt{{\frac{4}{.\dot{4}}}^{4}}\times4! ]
[ 1960 = {\sqrt{44}}^{4}+4! ]
[ 2000 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!}}{4} ]
[ 2016 = \left(4!+\frac{4!}{.4}\right)\times4! ]
[ 2024 = {\sqrt{\sqrt{\sqrt{4}}}}^{44}-4! ]
[ 2025 = \frac{4}{{\sqrt{\left(.\dot{4}-.4\right)}}^{4}} ]
[ 2036 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4!\right)}{\sqrt{4}} ]
[ 2039 = {\sqrt{4!}}^{\left(4+\sqrt{\sqrt{.4}}\right)}+\sqrt{\sqrt{.\dot{4}}} ]
[ 2044 = {\sqrt{\sqrt{\sqrt{4}}}}^{44}-4 ]
[ 2046 = {\sqrt{\sqrt{\sqrt{4}}}}^{44}-\sqrt{4} ]
[ 2047 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-\sqrt{4}\right)}{\sqrt{4}} ]
[ 2048 = \left(4+4\right)\times{4}^{4} ]
[ 2049 = \frac{\left(\sqrt{4}+{\sqrt{\sqrt{4}}}^{4!}\right)}{\sqrt{4}} ]
[ 2050 = \sqrt{4}+{\sqrt{\sqrt{\sqrt{4}}}}^{44} ]
[ 2052 = {\sqrt{\sqrt{\sqrt{4}}}}^{44}+4 ]
[ 2060 = \frac{\left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)}{\sqrt{4}} ]
[ 2072 = {\sqrt{\sqrt{\sqrt{4}}}}^{44}+4! ]
[ 2112 = \left(44\times\sqrt{4}\right)\times4! ]
[ 2116 = {\left(\sqrt{4}+44\right)}^{\sqrt{4}} ]
[ 2160 = \frac{4!}{\left(.\dot{4}-.4\right)}\times4 ]
[ 2187 = {\sqrt{\sqrt{\sqrt{\frac{4}{.\dot{4}}}}}}^{\left(4!+4\right)} ]
[ 2197 = {\sqrt{\sqrt{\sqrt{\left(\frac{4}{.\dot{4}}+4\right)}}}}^{4!} ]
[ 2208 = \left(\left(4!\times4\right)-4\right)\times4! ]
[ 2240 = \left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right)\times4 ]
[ 2250 = \frac{\sqrt{{\sqrt{\sqrt{\frac{4}{.4}}}}^{4!}}}{.\dot{4}} ]
[ 2256 = 4!\times\left(\left(4!\times4\right)-\sqrt{4}\right) ]
[ 2280 = \left(4!\times\left(4!\times4\right)\right)-4! ]
[ 2288 = 4\times\left(\left(4!\times4!\right)-4\right) ]
[ 2296 = \left(\left(4!\times4!\right)-\sqrt{4}\right)\times4 ]
[ 2300 = \left(4!\times\left(4!\times4\right)\right)-4 ]
[ 2302 = \left(4!\times\left(4!\times4\right)\right)-\sqrt{4} ]
[ 2304 = {\sqrt{\left(44+4\right)}}^{4} ]
[ 2306 = \sqrt{4}+\left(4!\times\left(4!\times4\right)\right) ]
[ 2308 = \left(4!\times\left(4!\times4\right)\right)+4 ]
[ 2312 = \left(\left(4!\times4!\right)+\sqrt{4}\right)\times4 ]
[ 2320 = 4\times\left(\left(4!\times4!\right)+4\right) ]
[ 2328 = \left(4!\times\left(4!\times4\right)\right)+4! ]
[ 2352 = 4!\times\left(\left(4!\times4\right)+\sqrt{4}\right) ]
[ 2368 = \left(\left(4!+\sqrt{.\dot{4}}\right)\times4\right)\times4! ]
[ 2376 = \frac{44}{.\dot{4}}\times4! ]
[ 2400 = 4!\times\left(4+\left(4!\times4\right)\right) ]
[ 2401 = {\frac{\left(4!+4\right)}{4}}^{4} ]
[ 2496 = \left(\left(\sqrt{4}+4!\right)\times4\right)\times4! ]
[ 2500 = \frac{{\frac{4}{.4}}^{4}}{4} ]
[ 2560 = \frac{{4}^{4}}{.4}\times4 ]
[ 2592 = {\left(4+\sqrt{4}\right)}^{4}\times\sqrt{4} ]
[ 2640 = \frac{\left(44\times4!\right)}{.4} ]
[ 2662 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}}{4} ]
[ 2688 = \left(\left(4!+4\right)\times4!\right)\times4 ]
[ 2704 = \sqrt{{\left(\sqrt{4}+4!\right)}^{4}}\times4 ]
[ 2728 = \left({\sqrt{\sqrt{4}}}^{4!}-4\right)\times\sqrt{.\dot{4}} ]
[ 2730 = \left({\sqrt{\sqrt{4}}}^{4!}\times\sqrt{.\dot{4}}\right)-\sqrt{.\dot{4}} ]
[ 2732 = \sqrt{.\dot{4}}\times\left(\sqrt{4}+{\sqrt{\sqrt{4}}}^{4!}\right) ]
[ 2744 = {\sqrt{\sqrt{\sqrt{\left(\frac{4}{.4}+4\right)}}}}^{4!} ]
[ 2809 = {\sqrt{\frac{\left(4!-.\dot{4}\right)}{.\dot{4}}}}^{4} ]
[ 2816 = 44\times{\sqrt{\sqrt{\sqrt{4}}}}^{4!} ]
[ 2880 = \left(4!+\left(4!\times4\right)\right)\times4! ]
[ 2892 = {\sqrt{\frac{4!}{.\dot{4}}}}^{4}-4! ]
[ 2904 = \frac{{\sqrt{44}}^{4}}{\sqrt{.\dot{4}}} ]
[ 2908 = {\left(\left(\sqrt{4}+\sqrt{4!}\right)+.\dot{4}\right)}^{4} ]
[ 2912 = {\sqrt{\frac{4!}{.\dot{4}}}}^{4}-4 ]
[ 2914 = {\sqrt{\frac{4!}{.\dot{4}}}}^{4}-\sqrt{4} ]
[ 2916 = .\dot{4}\times{\frac{4}{.\dot{4}}}^{4} ]
[ 2918 = \sqrt{4}+{\sqrt{\frac{4!}{.\dot{4}}}}^{4} ]
[ 2920 = 4+{\sqrt{\frac{4!}{.\dot{4}}}}^{4} ]
[ 2940 = 4!+{\sqrt{\frac{4!}{.\dot{4}}}}^{4} ]
[ 3000 = 4!\times{\sqrt{\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}}^{4!} ]
[ 3025 = {\sqrt{\frac{\left(4!+.\dot{4}\right)}{.\dot{4}}}}^{4} ]
[ 3072 = \frac{\left({4}^{4}\times4!\right)}{\sqrt{4}} ]
[ 3125 = {\sqrt{\frac{\sqrt{4}}{.4}}}^{\frac{4}{.4}} ]
[ 3136 = \sqrt{{\left(4!+4\right)}^{4}}\times4 ]
[ 3141 = {\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{\left(\sqrt{4!}-\sqrt{\sqrt{4!}}\right)}}}}}}^{4!} ]
[ 3200 = {\frac{4}{\sqrt{.4}}}^{4}\times\sqrt{4} ]
[ 3240 = \frac{{\left(4+\sqrt{4}\right)}^{4}}{.4} ]
[ 3364 = {\sqrt{\left(4+\frac{4!}{.\dot{4}}\right)}}^{4} ]
[ 3375 = {\sqrt{\sqrt{\sqrt{\frac{\left(4+\sqrt{4}\right)}{.4}}}}}^{4!} ]
[ 3456 = \frac{{4!}^{4}}{\left(4!\times4\right)} ]
[ 3481 = {\frac{\left(4!-.4\right)}{.4}}^{\sqrt{4}} ]
[ 3520 = {\sqrt{\sqrt{4}}}^{4!}-\left(4!\times4!\right) ]
[ 3576 = {\sqrt{\frac{4!}{.4}}}^{4}-4! ]
[ 3596 = {\sqrt{\frac{4!}{.4}}}^{4}-4 ]
[ 3598 = {\sqrt{\frac{4!}{.4}}}^{4}-\sqrt{4} ]
[ 3600 = \frac{{\frac{4}{\sqrt{.4}}}^{4}}{.\dot{4}} ]
[ 3602 = {\sqrt{\frac{4!}{.4}}}^{4}+\sqrt{4} ]
[ 3604 = {\sqrt{\frac{4!}{.4}}}^{4}+4 ]
[ 3624 = {\sqrt{\frac{4!}{.4}}}^{4}+4! ]
[ 3721 = {\sqrt{\frac{\left(4!+.4\right)}{.4}}}^{4} ]
[ 3750 = \frac{4!}{{.4}^{4}}\times4 ]
[ 3840 = {\sqrt{\sqrt{4}}}^{4!}-{4}^{4} ]
[ 3844 = {\left(\sqrt{4}+\frac{4!}{.4}\right)}^{\sqrt{4}} ]
[ 3872 = {\sqrt{44}}^{4}\times\sqrt{4} ]
[ 3888 = \frac{{\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{4}}}}}}^{4!}}{.\dot{4}} ]
[ 3969 = {\sqrt{\frac{\left(4!+4\right)}{.\dot{4}}}}^{4} ]
[ 4000 = .4\times{\frac{4}{.4}}^{4} ]
[ 4032 = {\sqrt{\sqrt{4}}}^{4!}-\sqrt{{\sqrt{\sqrt{4}}}^{4!}} ]
[ 4036 = {\sqrt{\sqrt{4}}}^{4!}-\frac{4!}{.4} ]
[ 4042 = {\sqrt{\sqrt{4}}}^{4!}-\frac{4!}{.\dot{4}} ]
[ 4048 = \left({\sqrt{\sqrt{4}}}^{4!}-4!\right)-4! ]
[ 4052 = {\sqrt{\sqrt{4}}}^{4!}-44 ]
[ 4060 = {\sqrt{\sqrt{4}}}^{4!}-\frac{4!}{\sqrt{.\dot{4}}} ]
[ 4068 = \left({\sqrt{\sqrt{4}}}^{4!}-4\right)-4! ]
[ 4070 = {\sqrt{\sqrt{4}}}^{4!}-\left(\sqrt{4}+4!\right) ]
[ 4072 = {\left(4+4\right)}^{4}-4! ]
[ 4074 = \left(\sqrt{4}+{\sqrt{\sqrt{4}}}^{4!}\right)-4! ]
[ 4076 = \left({\sqrt{\sqrt{4}}}^{4!}-4!\right)+4 ]
[ 4080 = {\sqrt{\sqrt{4}}}^{4!}-\left(4\times4\right) ]
[ 4084 = {\sqrt{\sqrt{4}}}^{4!}-\frac{4!}{\sqrt{4}} ]
[ 4086 = {\sqrt{\sqrt{4}}}^{4!}-\frac{4}{.4} ]
[ 4087 = {\sqrt{\sqrt{4}}}^{4!}-\frac{4}{.\dot{4}} ]
[ 4088 = {\sqrt{\sqrt{4}}}^{4!}-\left(4+4\right) ]
[ 4090 = {\sqrt{\sqrt{4}}}^{4!}-\left(4+\sqrt{4}\right) ]
[ 4091 = {\sqrt{\sqrt{4}}}^{4!}-\frac{\sqrt{4}}{.4} ]
[ 4092 = {\left(4+4\right)}^{4}-4 ]
[ 4093 = {\sqrt{\sqrt{4}}}^{4!}-\sqrt{\frac{4}{.\dot{4}}} ]
[ 4094 = {\left(4+4\right)}^{4}-\sqrt{4} ]
[ 4095 = {\sqrt{\sqrt{4}}}^{4!}-\frac{4}{4} ]
[ 4096 = \left({4}^{4}\times4\right)\times4 ]
[ 4097 = \frac{4}{4}+{\sqrt{\sqrt{4}}}^{4!} ]
[ 4098 = \sqrt{4}+{\left(4+4\right)}^{4} ]
[ 4099 = {\sqrt{\sqrt{4}}}^{4!}+\sqrt{\frac{4}{.\dot{4}}} ]
[ 4100 = {\left(4+4\right)}^{4}+4 ]
[ 4101 = \frac{\sqrt{4}}{.4}+{\sqrt{\sqrt{4}}}^{4!} ]
[ 4102 = \left(\sqrt{4}+{\sqrt{\sqrt{4}}}^{4!}\right)+4 ]
[ 4104 = \left({\sqrt{\sqrt{4}}}^{4!}+4\right)+4 ]
[ 4105 = {\sqrt{\sqrt{4}}}^{4!}+\frac{4}{.\dot{4}} ]
[ 4106 = {\sqrt{\sqrt{4}}}^{4!}+\frac{4}{.4} ]
[ 4108 = \frac{4!}{\sqrt{4}}+{\sqrt{\sqrt{4}}}^{4!} ]
[ 4112 = {\sqrt{\sqrt{4}}}^{4!}+\left(4\times4\right) ]
[ 4116 = \left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)-4 ]
[ 4118 = \left(4!-\sqrt{4}\right)+{\sqrt{\sqrt{4}}}^{4!} ]
[ 4120 = {\left(4+4\right)}^{4}+4! ]
[ 4122 = \left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)+\sqrt{4} ]
[ 4124 = \left({\sqrt{\sqrt{4}}}^{4!}+4\right)+4! ]
[ 4132 = \frac{4!}{\sqrt{.\dot{4}}}+{\sqrt{\sqrt{4}}}^{4!} ]
[ 4140 = {\sqrt{\sqrt{4}}}^{4!}+44 ]
[ 4144 = \left(4!\times\sqrt{4}\right)+{\sqrt{\sqrt{4}}}^{4!} ]
[ 4150 = {\sqrt{\sqrt{4}}}^{4!}+\frac{4!}{.\dot{4}} ]
[ 4156 = {\sqrt{\sqrt{4}}}^{4!}+\frac{4!}{.4} ]
[ 4160 = {\sqrt{\sqrt{4}}}^{4!}+\sqrt{{\sqrt{\sqrt{4}}}^{4!}} ]
[ 4192 = \left(4!\times4\right)+{\sqrt{\sqrt{4}}}^{4!} ]
[ 4224 = \left(4!\times4\right)\times44 ]
[ 4225 = {\frac{\left(\sqrt{4}+4!\right)}{.4}}^{\sqrt{4}} ]
[ 4320 = \frac{{\sqrt{\sqrt{\sqrt{\frac{4!}{\sqrt{4}}}}}}^{4!}}{.4} ]
[ 4352 = {\sqrt{\sqrt{4}}}^{4!}+{4}^{4} ]
[ 4356 = \frac{{\sqrt{44}}^{4}}{.\dot{4}} ]
[ 4374 = {\frac{4}{.\dot{4}}}^{4}\times\sqrt{.\dot{4}} ]
[ 4394 = \frac{{\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}}{4} ]
[ 4444 = 4444 ]
[ 4608 = \left(4!\times4!\right)\times\left(4+4\right) ]
[ 4624 = {\sqrt{\left(44+4!\right)}}^{4} ]
[ 4672 = \left(4!\times4!\right)+{\sqrt{\sqrt{4}}}^{4!} ]
[ 4840 = \frac{{\sqrt{44}}^{4}}{.4} ]
[ 4900 = {\sqrt{\frac{\left(4!+4\right)}{.4}}}^{4} ]
[ 5000 = \frac{{\frac{4}{.4}}^{4}}{\sqrt{4}} ]
[ 5120 = {4}^{4}\times\left(4!-4\right) ]
[ 5184 = 4\times{\left(4+\sqrt{4}\right)}^{4} ]
[ 5324 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}}{\sqrt{4}} ]
[ 5400 = \frac{{\sqrt{\frac{4!}{.4}}}^{4}}{\sqrt{.\dot{4}}} ]
[ 5488 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}}{4} ]
[ 5568 = \left({4}^{4}-4!\right)\times4! ]
[ 5625 = \frac{{\frac{\sqrt{4!}}{.4}}^{4}}{4} ]
[ 5632 = \left(4!-\sqrt{4}\right)\times{4}^{4} ]
[ 5760 = \frac{{4}^{4}}{\left(.\dot{4}-.4\right)} ]
[ 5832 = \sqrt{4}\times{\sqrt{\frac{4!}{.\dot{4}}}}^{4} ]
[ 6048 = \left({4}^{4}-4\right)\times4! ]
[ 6084 = {\left(4!+\frac{4!}{.\dot{4}}\right)}^{\sqrt{4}} ]
[ 6096 = \left({4}^{4}-\sqrt{4}\right)\times4! ]
[ 6108 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4!\right)}{\sqrt{.\dot{4}}} ]
[ 6120 = \left({4}^{4}\times4!\right)-4! ]
[ 6128 = \left({4}^{4}-\sqrt{.\dot{4}}\right)\times4! ]
[ 6138 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4\right)}{\sqrt{.\dot{4}}} ]
[ 6140 = \left({4}^{4}\times4!\right)-4 ]
[ 6141 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-\sqrt{4}\right)}{\sqrt{.\dot{4}}} ]
[ 6142 = \left({4}^{4}\times4!\right)-\sqrt{4} ]
[ 6143 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-\sqrt{.\dot{4}}\right)}{\sqrt{.\dot{4}}} ]
[ 6144 = \frac{{\left(4+4\right)}^{4}}{\sqrt{.\dot{4}}} ]
[ 6145 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}+\sqrt{.\dot{4}}\right)}{\sqrt{.\dot{4}}} ]
[ 6146 = \left({4}^{4}\times4!\right)+\sqrt{4} ]
[ 6147 = \frac{\left(\sqrt{4}+{\sqrt{\sqrt{4}}}^{4!}\right)}{\sqrt{.\dot{4}}} ]
[ 6148 = \left({4}^{4}\times4!\right)+4 ]
[ 6150 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}+4\right)}{\sqrt{.\dot{4}}} ]
[ 6160 = \left({4}^{4}+\sqrt{.\dot{4}}\right)\times4! ]
[ 6168 = \left({4}^{4}\times4!\right)+4! ]
[ 6180 = \frac{\left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)}{\sqrt{.\dot{4}}} ]
[ 6192 = \left({4}^{4}+\sqrt{4}\right)\times4! ]
[ 6240 = 4!\times\left({4}^{4}+4\right) ]
[ 6250 = {\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{4!}\times.4 ]
[ 6400 = 4\times{\frac{4}{\sqrt{.4}}}^{4} ]
[ 6537 = {\frac{4}{.\dot{4}}}^{4}-4! ]
[ 6557 = {\frac{4}{.\dot{4}}}^{4}-4 ]
[ 6559 = {\frac{4}{.\dot{4}}}^{4}-\sqrt{4} ]
[ 6561 = {\frac{\left(4-.4\right)}{.4}}^{4} ]
[ 6563 = \sqrt{4}+{\frac{4}{.\dot{4}}}^{4} ]
[ 6565 = {\frac{4}{.\dot{4}}}^{4}+4 ]
[ 6585 = {\frac{4}{.\dot{4}}}^{4}+4! ]
[ 6656 = \left(\sqrt{4}+4!\right)\times{4}^{4} ]
[ 6720 = 4!\times\left({4}^{4}+4!\right) ]
[ 6859 = {\sqrt{\sqrt{\sqrt{\left(4!-\frac{\sqrt{4}}{.4}\right)}}}}^{4!} ]
[ 6912 = 4!\times\sqrt{\frac{{4!}^{4}}{4}} ]
[ 7056 = {\left(4!+\frac{4!}{.4}\right)}^{\sqrt{4}} ]
[ 7168 = \left(4!+4\right)\times{4}^{4} ]
[ 7200 = {\sqrt{\frac{4!}{.4}}}^{4}\times\sqrt{4} ]
[ 7290 = \frac{{\sqrt{\frac{4!}{.\dot{4}}}}^{4}}{.4} ]
[ 7744 = 4\times{\sqrt{44}}^{4} ]
[ 7776 = {\sqrt{\left(4+\sqrt{4}\right)}}^{\frac{4}{.4}} ]
[ 7976 = {\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!}-4! ]
[ 7996 = {\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!}-4 ]
[ 7998 = {\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!}-\sqrt{4} ]
[ 8000 = {\left(4!-4\right)}^{\sqrt{\frac{4}{.\dot{4}}}} ]
[ 8002 = \sqrt{4}+{\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!} ]
[ 8004 = 4+{\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!} ]
[ 8024 = 4!+{\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!} ]
[ 8100 = {\frac{4}{\left(.\dot{4}-.4\right)}}^{\sqrt{4}} ]
[ 8144 = \left({\sqrt{\sqrt{4}}}^{4!}-4!\right)\times\sqrt{4} ]
[ 8168 = {\sqrt{\sqrt{4}}}^{\left(\sqrt{4}+4!\right)}-4! ]
[ 8184 = \left({\sqrt{\sqrt{4}}}^{4!}-4\right)\times\sqrt{4} ]
[ 8188 = {\sqrt{\sqrt{4}}}^{\left(\sqrt{4}+4!\right)}-4 ]
[ 8190 = {\sqrt{\sqrt{4}}}^{\left(\sqrt{4}+4!\right)}-\sqrt{4} ]
[ 8192 = \sqrt{4}\times{\left(4+4\right)}^{4} ]
[ 8194 = \sqrt{4}+{\sqrt{\sqrt{4}}}^{\left(\sqrt{4}+4!\right)} ]
[ 8196 = 4+{\sqrt{\sqrt{4}}}^{\left(\sqrt{4}+4!\right)} ]
[ 8200 = \sqrt{4}\times\left({\sqrt{\sqrt{4}}}^{4!}+4\right) ]
[ 8216 = {\sqrt{\sqrt{4}}}^{\left(\sqrt{4}+4!\right)}+4! ]
[ 8240 = \sqrt{4}\times\left(4!+{\sqrt{\sqrt{4}}}^{4!}\right) ]
[ 8464 = {\sqrt{\left(\left(4!\times4\right)-4\right)}}^{4} ]
[ 8788 = \frac{{\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}}{\sqrt{4}} ]
[ 8836 = {\left(\left(4!\times4\right)-\sqrt{4}\right)}^{\sqrt{4}} ]
[ 9000 = {\frac{\sqrt{4!}}{.4}}^{4}\times.4 ]
[ 9162 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4!\right)}{.\dot{4}} ]
[ 9192 = {\sqrt{\left(4!\times4\right)}}^{4}-4! ]
[ 9207 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4\right)}{.\dot{4}} ]
[ 9212 = {\sqrt{\left(4!\times4\right)}}^{4}-4 ]
[ 9214 = {\sqrt{\left(4!\times4\right)}}^{4}-\sqrt{4} ]
[ 9215 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-.\dot{4}\right)}{.\dot{4}} ]
[ 9216 = \frac{{\left(4+4\right)}^{4}}{.\dot{4}} ]
[ 9217 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}+.\dot{4}\right)}{.\dot{4}} ]
[ 9218 = \sqrt{4}+{\sqrt{\left(4!\times4\right)}}^{4} ]
[ 9220 = {\sqrt{\left(4!\times4\right)}}^{4}+4 ]
[ 9225 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}+4\right)}{.\dot{4}} ]
[ 9240 = 4!+{\sqrt{\left(4!\times4\right)}}^{4} ]
[ 9261 = {\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{\frac{4}{.\dot{4}}}\right)}}}}^{4!} ]
[ 9270 = \frac{\left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)}{.\dot{4}} ]
[ 9600 = \sqrt{{\left(4!-4\right)}^{4}}\times4! ]
[ 9604 = {\sqrt{\left(\left(4!\times4\right)+\sqrt{4}\right)}}^{4} ]
[ 9801 = {\frac{44}{.\dot{4}}}^{\sqrt{4}} ]
[ 9976 = {\frac{4}{.4}}^{4}-4! ]
[ 9996 = {\frac{4}{.4}}^{4}-4 ]
[ 9998 = {\frac{4}{.4}}^{4}-\sqrt{4} ]
[ 10000 = {\frac{\left(.\dot{4}+4\right)}{.\dot{4}}}^{4} ]
[ 10002 = \sqrt{4}+{\frac{4}{.4}}^{4} ]
[ 10004 = 4+{\frac{4}{.4}}^{4} ]
[ 10024 = {\frac{4}{.4}}^{4}+4! ]
[ 10180 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4!\right)}{.4} ]
[ 10216 = \frac{{\sqrt{\sqrt{4}}}^{4!}}{.4}-4! ]
[ 10230 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-4\right)}{.4} ]
[ 10235 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-\sqrt{4}\right)}{.4} ]
[ 10236 = \frac{{\sqrt{\sqrt{4}}}^{4!}}{.4}-4 ]
[ 10238 = \frac{{\sqrt{\sqrt{4}}}^{4!}}{.4}-\sqrt{4} ]
[ 10239 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}-.4\right)}{.4} ]
[ 10240 = \frac{{\left(4+4\right)}^{4}}{.4} ]
[ 10241 = \frac{\left(.4+{\sqrt{\sqrt{4}}}^{4!}\right)}{.4} ]
[ 10242 = \sqrt{4}+\frac{{\sqrt{\sqrt{4}}}^{4!}}{.4} ]
[ 10244 = 4+\frac{{\sqrt{\sqrt{4}}}^{4!}}{.4} ]
[ 10245 = \frac{\left(\sqrt{4}+{\sqrt{\sqrt{4}}}^{4!}\right)}{.4} ]
[ 10250 = \frac{\left({\sqrt{\sqrt{4}}}^{4!}+4\right)}{.4} ]
[ 10264 = 4!+\frac{{\sqrt{\sqrt{4}}}^{4!}}{.4} ]
[ 10300 = \frac{\left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)}{.4} ]
[ 10368 = \frac{{\frac{4!}{\sqrt{4}}}^{4}}{\sqrt{4}} ]
[ 10624 = {\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}-4! ]
[ 10644 = {\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}-4 ]
[ 10646 = {\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}-\sqrt{4} ]
[ 10648 = {\left(4!-\sqrt{4}\right)}^{\sqrt{\frac{4}{.\dot{4}}}} ]
[ 10650 = {\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}+\sqrt{4} ]
[ 10652 = 4+{\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!} ]
[ 10656 = 444\times4! ]
[ 10672 = 4!+{\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!} ]
[ 10816 = {\sqrt{\left(\left(\sqrt{4}+4!\right)\times4\right)}}^{4} ]
[ 10976 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}}{\sqrt{4}} ]
[ 11250 = \frac{{\frac{\sqrt{4!}}{.4}}^{4}}{\sqrt{4}} ]
[ 11264 = {4}^{4}\times44 ]
[ 11520 = 4!\times\left(4!\times\left(4!-4\right)\right) ]
[ 11616 = 4!\times\sqrt{{\left(4!-\sqrt{4}\right)}^{4}} ]
[ 11664 = 4\times{\sqrt{\frac{4!}{.\dot{4}}}}^{4} ]
[ 12000 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!}}{\sqrt{.\dot{4}}} ]
[ 12100 = {\frac{44}{.4}}^{\sqrt{4}} ]
[ 12150 = \frac{4!}{{\sqrt{\left(.\dot{4}-.4\right)}}^{4}} ]
[ 12167 = {\sqrt{\sqrt{\sqrt{\left(4!-\frac{4}{4}\right)}}}}^{4!} ]
[ 12288 = \left({4}^{4}\times4!\right)\times\sqrt{4} ]
[ 12544 = {\left(\left(4!+4\right)\times4\right)}^{\sqrt{4}} ]
[ 12672 = 4!\times\left(4!\times\left(4!-\sqrt{4}\right)\right) ]
[ 12696 = {\sqrt{\left(\left(4!\times\sqrt{4!}\right)-\sqrt{4!}\right)}}^{4} ]
[ 12960 = 4!\times\frac{4!}{\left(.\dot{4}-.4\right)} ]
[ 13122 = {\frac{4}{.\dot{4}}}^{4}\times\sqrt{4} ]
[ 13248 = 4!\times\left(\left(4!\times4!\right)-4!\right) ]
[ 13440 = \left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right)\times4! ]
[ 13568 = \left(4!-.\dot{4}\right)\times\left(4!\times4!\right) ]
[ 13728 = \left(\left(4!\times4!\right)-4\right)\times4! ]
[ 13776 = 4!\times\left(\left(4!\times4!\right)-\sqrt{4}\right) ]
[ 13800 = \frac{{4!}^{4}}{4!}-4! ]
[ 13808 = \left(\left(4!\times4!\right)-\sqrt{.\dot{4}}\right)\times4! ]
[ 13820 = \frac{{4!}^{4}}{4!}-4 ]
[ 13822 = \frac{{4!}^{4}}{4!}-\sqrt{4} ]
[ 13823 = \frac{\left({4!}^{4}-4!\right)}{4!} ]
[ 13824 = {4!}^{\left(4-\frac{4}{4}\right)} ]
[ 13825 = \frac{\left({4!}^{4}+4!\right)}{4!} ]
[ 13826 = \frac{{4!}^{4}}{4!}+\sqrt{4} ]
[ 13828 = \frac{{4!}^{4}}{4!}+4 ]
[ 13840 = 4!\times\left(\sqrt{.\dot{4}}+\left(4!\times4!\right)\right) ]
[ 13848 = 4!+\frac{{4!}^{4}}{4!} ]
[ 13872 = \left(\left(4!\times4!\right)+\sqrt{4}\right)\times4! ]
[ 13920 = 4!\times\left(\left(4!\times4!\right)+4\right) ]
[ 14080 = 4!\times\left(\left(4!+.\dot{4}\right)\times4!\right) ]
[ 14208 = 4!\times\left(4!\times\left(4!+\sqrt{.\dot{4}}\right)\right) ]
[ 14400 = {\sqrt{\frac{4!}{.4}}}^{4}\times4 ]
[ 14641 = {\frac{44}{4}}^{4} ]
[ 14976 = \left(\sqrt{4}+4!\right)\times\left(4!\times4!\right) ]
[ 15000 = \frac{{\frac{4}{.4}}^{4}}{\sqrt{.\dot{4}}} ]
[ 15360 = 4!\times\frac{{4}^{4}}{.4} ]
[ 15601 = {\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{4!}-4! ]
[ 15621 = {\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{4!}-4 ]
[ 15623 = {\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{4!}-\sqrt{4} ]
[ 15625 = {\frac{\sqrt{\left(4!-4\right)}}{.4}}^{4} ]
[ 15627 = {\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{4!}+\sqrt{4} ]
[ 15629 = {\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{4!}+4 ]
[ 15649 = 4!+{\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{4!} ]
[ 15972 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}}{\sqrt{.\dot{4}}} ]
[ 16000 = \frac{{\sqrt{\sqrt{\frac{4}{\sqrt{.4}}}}}^{4!}}{4} ]
[ 16128 = \left(4!\times4!\right)\times\left(4!+4\right) ]
[ 16224 = \sqrt{{\left(\sqrt{4}+4!\right)}^{4}}\times4! ]
[ 16288 = 4\times\left({\sqrt{\sqrt{4}}}^{4!}-4!\right) ]
[ 16360 = {\sqrt{\sqrt{4}}}^{\left(4!+4\right)}-4! ]
[ 16368 = \left({\sqrt{\sqrt{4}}}^{4!}-4\right)\times4 ]
[ 16376 = 4\times\left({\sqrt{\sqrt{4}}}^{4!}-\sqrt{4}\right) ]
[ 16380 = {\sqrt{\sqrt{4}}}^{\left(4!+4\right)}-4 ]
[ 16382 = {\sqrt{\sqrt{4}}}^{\left(4!+4\right)}-\sqrt{4} ]
[ 16384 = 4\times{\left(4+4\right)}^{4} ]
[ 16386 = \sqrt{4}+{\sqrt{\sqrt{4}}}^{\left(4!+4\right)} ]
[ 16388 = 4+{\sqrt{\sqrt{4}}}^{\left(4!+4\right)} ]
[ 16392 = 4\times\left(\sqrt{4}+{\sqrt{\sqrt{4}}}^{4!}\right) ]
[ 16400 = 4\times\left({\sqrt{\sqrt{4}}}^{4!}+4\right) ]
[ 16408 = {\sqrt{\sqrt{4}}}^{\left(4!+4\right)}+4! ]
[ 16480 = \left(4!+{\sqrt{\sqrt{4}}}^{4!}\right)\times4 ]
[ 17496 = 4!\times\sqrt{{\sqrt{\sqrt{\frac{4}{.\dot{4}}}}}^{4!}} ]
[ 17552 = {\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}-4! ]
[ 17572 = {\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}-4 ]
[ 17574 = {\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}-\sqrt{4} ]
[ 17576 = {\left(\sqrt{4}+4!\right)}^{\sqrt{\frac{4}{.\dot{4}}}} ]
[ 17578 = {\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}+\sqrt{4} ]
[ 17580 = {\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}+4 ]
[ 17600 = {\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}+4! ]
[ 18000 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!}}{.\dot{4}} ]
[ 18225 = {\frac{4!}{\left(.\dot{4}\times.4\right)}}^{\sqrt{4}} ]
[ 18432 = {\sqrt{\left(4!\times4\right)}}^{4}\times\sqrt{4} ]
[ 18816 = {\left(4!+4\right)}^{\sqrt{4}}\times4! ]
[ 19683 = {\sqrt{\frac{4}{.\dot{4}}}}^{\frac{4}{.\dot{4}}} ]
[ 20000 = {\frac{4}{.4}}^{4}\times\sqrt{4} ]
[ 20480 = \frac{{\sqrt{\sqrt{4}}}^{4!}}{.4}\times\sqrt{4} ]
[ 20712 = {\frac{4!}{\sqrt{4}}}^{4}-4! ]
[ 20732 = {\frac{4!}{\sqrt{4}}}^{4}-4 ]
[ 20734 = {\frac{4!}{\sqrt{4}}}^{4}-\sqrt{4} ]
[ 20736 = {\left(4+\left(4+4\right)\right)}^{4} ]
[ 20738 = {\frac{4!}{\sqrt{4}}}^{4}+\sqrt{4} ]
[ 20740 = {\frac{4!}{\sqrt{4}}}^{4}+4 ]
[ 20760 = 4!+{\frac{4!}{\sqrt{4}}}^{4} ]
[ 21296 = \frac{{\sqrt{\sqrt{\sqrt{44}}}}^{4!}}{4} ]
[ 21928 = {\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}-4! ]
[ 21948 = {\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}-4 ]
[ 21950 = {\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}-\sqrt{4} ]
[ 21952 = {\left(4!+4\right)}^{\sqrt{\frac{4}{.\dot{4}}}} ]
[ 21954 = \sqrt{4}+{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!} ]
[ 21956 = 4+{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!} ]
[ 21976 = 4!+{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!} ]
[ 22476 = {\frac{\sqrt{4!}}{.4}}^{4}-4! ]
[ 22496 = {\frac{\sqrt{4!}}{.4}}^{4}-4 ]
[ 22498 = {\frac{\sqrt{4!}}{.4}}^{4}-\sqrt{4} ]
[ 22500 = \frac{{\frac{4}{.4}}^{4}}{.\dot{4}} ]
[ 22502 = \sqrt{4}+{\frac{\sqrt{4!}}{.4}}^{4} ]
[ 22504 = 4+{\frac{\sqrt{4!}}{.4}}^{4} ]
[ 22524 = {\frac{\sqrt{4!}}{.4}}^{4}+4! ]
[ 23040 = \frac{{\sqrt{\left(4!\times4\right)}}^{4}}{.4} ]
[ 23328 = \frac{{\sqrt{\sqrt{\left(4+\sqrt{4}\right)}}}^{4!}}{\sqrt{4}} ]
[ 23958 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}}{.\dot{4}} ]
[ 24000 = {\sqrt{\sqrt{\sqrt{\frac{4}{.4}}}}}^{4!}\times4! ]
[ 24389 = {\sqrt{\sqrt{\sqrt{\left(4!+\frac{\sqrt{4}}{.4}\right)}}}}^{4!} ]
[ 24576 = \left({4}^{4}\times4\right)\times4! ]
[ 25000 = \frac{{\frac{4}{.4}}^{4}}{.4} ]
[ 25344 = \left(4!\times4!\right)\times44 ]
[ 25600 = {\frac{\left(4+4\right)}{\sqrt{.4}}}^{4} ]
[ 26244 = 4\times{\frac{4}{.\dot{4}}}^{4} ]
[ 26364 = \frac{{\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}}{\sqrt{.\dot{4}}} ]
[ 26620 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}}^{4!}}{.4} ]
[ 27000 = {\sqrt{\sqrt{\sqrt{\frac{4!}{\left(.4+.4\right)}}}}}^{4!} ]
[ 27648 = \frac{{4!}^{4}}{4!}\times\sqrt{4} ]
[ 28561 = {\left(\frac{4}{.\dot{4}}+4\right)}^{4} ]
[ 30625 = {\frac{\sqrt{\left(4!+4\right)}}{.4}}^{4} ]
[ 30976 = {\sqrt{\left(4\times44\right)}}^{4} ]
[ 31104 = {\left(4+\sqrt{4}\right)}^{4}\times4! ]
[ 31250 = \sqrt{4}\times{\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{4!} ]
[ 32000 = 4\times{\sqrt{\sqrt{\sqrt{\left(4!-4\right)}}}}^{4!} ]
[ 32744 = {\sqrt{\sqrt{\sqrt{4}}}}^{\frac{4!}{.4}}-4! ]
[ 32764 = {\sqrt{\sqrt{\sqrt{4}}}}^{\frac{4!}{.4}}-4 ]
[ 32766 = {\sqrt{\sqrt{\sqrt{4}}}}^{\frac{4!}{.4}}-\sqrt{4} ]
[ 32768 = \frac{{\left(4\times4\right)}^{4}}{\sqrt{4}} ]
[ 32770 = {\sqrt{\sqrt{\sqrt{4}}}}^{\frac{4!}{.4}}+\sqrt{4} ]
[ 32772 = 4+{\sqrt{\sqrt{\sqrt{4}}}}^{\frac{4!}{.4}} ]
[ 32792 = 4!+{\sqrt{\sqrt{\sqrt{4}}}}^{\frac{4!}{.4}} ]
[ 32928 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}}{\sqrt{.\dot{4}}} ]
[ 33750 = \frac{{\frac{\sqrt{4!}}{.4}}^{4}}{\sqrt{.\dot{4}}} ]
[ 34560 = \frac{{4!}^{4}}{\left(4!\times.4\right)} ]
[ 35152 = \sqrt{4}\times{\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!} ]
[ 35937 = {\sqrt{\frac{\sqrt{\sqrt{\left(4!-\sqrt{4}\right)}}}{\sqrt{\sqrt{\sqrt{.\dot{4}}}}}}}^{4!} ]
[ 36864 = {4!}^{4}\times\frac{.\dot{4}}{4} ]
[ 38400 = 4!\times{\frac{4}{\sqrt{.4}}}^{4} ]
[ 38416 = {\left(\frac{4}{.4}+4\right)}^{4} ]
[ 39304 = {\sqrt{\sqrt{\sqrt{\left(4!+\frac{4}{.4}\right)}}}}^{4!} ]
[ 39366 = \frac{{\sqrt{\sqrt{\sqrt{\frac{4!}{.\dot{4}}}}}}^{4!}}{4} ]
[ 39546 = \frac{{\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}}{.\dot{4}} ]
[ 40000 = {\frac{4}{.4}}^{4}\times4 ]
[ 40960 = 4\times\frac{{\sqrt{\sqrt{4}}}^{4!}}{.4} ]
[ 41472 = \frac{{4!}^{4}}{\left(4+4\right)} ]
[ 42592 = \frac{{\sqrt{\sqrt{\sqrt{44}}}}^{4!}}{\sqrt{4}} ]
[ 42875 = {\sqrt{\sqrt{\sqrt{\frac{\left(4!-\sqrt{.\dot{4}}\right)}{\sqrt{.\dot{4}}}}}}}^{4!} ]
[ 43904 = {\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}\times\sqrt{4} ]
[ 43940 = \frac{{\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}}{.4} ]
[ 45000 = {\frac{\sqrt{4!}}{.4}}^{4}\times\sqrt{4} ]
[ 46464 = {\sqrt{44}}^{4}\times4! ]
[ 46632 = {\sqrt{\sqrt{\left(4+\sqrt{4}\right)}}}^{4!}-4! ]
[ 46652 = {\sqrt{\sqrt{\left(4+\sqrt{4}\right)}}}^{4!}-4 ]
[ 46654 = {\sqrt{\sqrt{\left(4+\sqrt{4}\right)}}}^{4!}-\sqrt{4} ]
[ 46656 = {\left(4+\sqrt{4}\right)}^{\left(4+\sqrt{4}\right)} ]
[ 46658 = \sqrt{4}+{\sqrt{\sqrt{\left(4+\sqrt{4}\right)}}}^{4!} ]
[ 46660 = 4+{\sqrt{\sqrt{\left(4+\sqrt{4}\right)}}}^{4!} ]
[ 46680 = {\sqrt{\sqrt{\left(4+\sqrt{4}\right)}}}^{4!}+4! ]
[ 46875 = 4!\times{\sqrt{\sqrt{\frac{\sqrt{\sqrt{4}}}{.4}}}}^{4!} ]
[ 49152 = {\sqrt{\sqrt{\sqrt{4}}}}^{44}\times4! ]
[ 49392 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}}{.\dot{4}} ]
[ 50625 = {\frac{\left(4+\sqrt{4}\right)}{.4}}^{4} ]
[ 50653 = {\sqrt{\sqrt{\frac{\sqrt{\left(4!+\sqrt{.\dot{4}}\right)}}{\sqrt{\sqrt{.\dot{4}}}}}}}^{4!} ]
[ 51840 = \frac{{\frac{4!}{\sqrt{4}}}^{4}}{.4} ]
[ 53824 = {\left({4}^{4}-4!\right)}^{\sqrt{4}} ]
[ 54000 = \frac{{\sqrt{\sqrt{\sqrt{\frac{4!}{.4}}}}}^{4!}}{4} ]
[ 54872 = {\sqrt{\sqrt{\sqrt{\left(\frac{4!}{\sqrt{.\dot{4}}}+\sqrt{4}\right)}}}}^{4!} ]
[ 54880 = \frac{{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!}}{.4} ]
[ 55296 = \frac{{4!}^{4}}{\left(4+\sqrt{4}\right)} ]
[ 56250 = \frac{{\frac{\sqrt{4!}}{.4}}^{4}}{.4} ]
[ 57600 = {\left(\frac{4}{.4}\times4!\right)}^{\sqrt{4}} ]
[ 58564 = \frac{{\left(4!-\sqrt{4}\right)}^{4}}{4} ]
[ 59049 = {\frac{4}{.\dot{4}}}^{\frac{\sqrt{4}}{.4}} ]
[ 59319 = {\sqrt{\sqrt{\sqrt{\frac{\left(\sqrt{4}+4!\right)}{\sqrt{.\dot{4}}}}}}}^{4!} ]
[ 62500 = {\frac{4}{\left(\sqrt{.4}\times.4\right)}}^{4} ]
[ 63504 = {\left({4}^{4}-4\right)}^{\sqrt{4}} ]
[ 63976 = {\sqrt{\sqrt{\frac{4}{\sqrt{.4}}}}}^{4!}-4! ]
[ 63996 = {\sqrt{\sqrt{\frac{4}{\sqrt{.4}}}}}^{4!}-4 ]
[ 63998 = {\sqrt{\sqrt{\frac{4}{\sqrt{.4}}}}}^{4!}-\sqrt{4} ]
[ 64000 = {\left(4!-4\right)}^{4}\times.4 ]
[ 64002 = {\sqrt{\sqrt{\frac{4}{\sqrt{.4}}}}}^{4!}+\sqrt{4} ]
[ 64004 = 4+{\sqrt{\sqrt{\frac{4}{\sqrt{.4}}}}}^{4!} ]
[ 64024 = 4!+{\sqrt{\sqrt{\frac{4}{\sqrt{.4}}}}}^{4!} ]
[ 64516 = {\left({4}^{4}-\sqrt{4}\right)}^{\sqrt{4}} ]
[ 65512 = {\left(4\times4\right)}^{4}-4! ]
[ 65532 = {\left(4\times4\right)}^{4}-4 ]
[ 65534 = {\left(4\times4\right)}^{4}-\sqrt{4} ]
[ 65536 = {4}^{4}\times{4}^{4} ]
[ 65538 = \sqrt{4}+{\left(4\times4\right)}^{4} ]
[ 65540 = {\left(4\times4\right)}^{4}+4 ]
[ 65560 = {\left(4\times4\right)}^{4}+4! ]
[ 66564 = {\sqrt{\left({4}^{4}+\sqrt{4}\right)}}^{4} ]
[ 67600 = {\left({4}^{4}+4\right)}^{\sqrt{4}} ]
[ 69984 = 4!\times{\sqrt{\frac{4!}{.\dot{4}}}}^{4} ]
[ 70304 = {\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+4!\right)}}}}^{4!}\times4 ]
[ 73728 = \frac{{4!}^{4}}{\sqrt{4}}\times.\dot{4} ]
[ 74088 = {\sqrt{\sqrt{\sqrt{\left(44-\sqrt{4}\right)}}}}^{4!} ]
[ 75625 = {\frac{\sqrt{44}}{.4}}^{4} ]
[ 78125 = {\sqrt{\sqrt{\frac{\sqrt{4}}{.4}}}}^{\left(4!+4\right)} ]
[ 78400 = {\sqrt{\left({4}^{4}+4!\right)}}^{4} ]
[ 78732 = \frac{{\sqrt{\sqrt{\sqrt{\frac{4!}{.\dot{4}}}}}}^{4!}}{\sqrt{4}} ]
[ 80000 = \frac{{\left(4!-4\right)}^{4}}{\sqrt{4}} ]
[ 81920 = {\sqrt{\sqrt{4}}}^{4!}\times\left(4!-4\right) ]
[ 82920 = \frac{{4!}^{4}}{4}-4! ]
[ 82938 = \frac{\left({4!}^{4}-4!\right)}{4} ]
[ 82940 = \frac{{4!}^{4}}{4}-4 ]
[ 82942 = \frac{{4!}^{4}}{4}-\sqrt{4} ]
[ 82943 = \frac{\left({4!}^{4}-4\right)}{4} ]
[ 82944 = 4\times{\frac{4!}{\sqrt{4}}}^{4} ]
[ 82945 = \frac{\left({4!}^{4}+4\right)}{4} ]
[ 82946 = \frac{{4!}^{4}}{4}+\sqrt{4} ]
[ 82948 = \frac{{4!}^{4}}{4}+4 ]
[ 82950 = \frac{\left({4!}^{4}+4!\right)}{4} ]
[ 82968 = \frac{{4!}^{4}}{4}+4! ]
[ 85160 = {\sqrt{\sqrt{\sqrt{44}}}}^{4!}-4! ]
[ 85180 = {\sqrt{\sqrt{\sqrt{44}}}}^{4!}-4 ]
[ 85182 = {\sqrt{\sqrt{\sqrt{44}}}}^{4!}-\sqrt{4} ]
[ 85184 = {44}^{\sqrt{\frac{4}{.\dot{4}}}} ]
[ 85186 = \sqrt{4}+{\sqrt{\sqrt{\sqrt{44}}}}^{4!} ]
[ 85188 = {\sqrt{\sqrt{\sqrt{44}}}}^{4!}+4 ]
[ 85208 = {\sqrt{\sqrt{\sqrt{44}}}}^{4!}+4! ]
[ 86400 = 4!\times{\sqrt{\frac{4!}{.4}}}^{4} ]
[ 86436 = {\left(\frac{\sqrt{4!}}{.4}+\sqrt{4!}\right)}^{4} ]
[ 87808 = 4\times{\sqrt{\sqrt{\sqrt{\left(4!+4\right)}}}}^{4!} ]
[ 90000 = 4\times{\frac{\sqrt{4!}}{.4}}^{4} ]
[ 90112 = {\sqrt{\sqrt{4}}}^{4!}\times\left(4!-\sqrt{4}\right) ]
[ 91125 = {\sqrt{\sqrt{\sqrt{\frac{\left(4!-4\right)}{.\dot{4}}}}}}^{4!} ]
[ 92160 = \frac{{4!}^{4}}{\left(4-.4\right)} ]
[ 93312 = \frac{{4!}^{4}}{\left(4-.\dot{4}\right)} ]
[ 96000 = .\dot{4}\times{\sqrt{\sqrt{\sqrt{\frac{4!}{.4}}}}}^{4!} ]
[ 97336 = {\sqrt{\sqrt{\sqrt{\left(\sqrt{4}+44\right)}}}}^{4!} ]
[ 97728 = 4!\times\left({\sqrt{\sqrt{4}}}^{4!}-4!\right) ]
[ 98208 = 4!\times\left({\sqrt{\sqrt{4}}}^{4!}-4\right) ]
[ 98256 = 4!\times\left({\sqrt{\sqrt{4}}}^{4!}-\sqrt{4}\right) ]
[ 98280 = \left(4!\times{\sqrt{\sqrt{4}}}^{4!}\right)-4! ]
[ 98288 = 4!\times\left({\sqrt{\sqrt{4}}}^{4!}-\sqrt{.\dot{4}}\right) ]
[ 98300 = \left(4!\times{\sqrt{\sqrt{4}}}^{4!}\right)-4 ]
[ 98302 = \left(4!\times{\sqrt{\sqrt{4}}}^{4!}\right)-\sqrt{4} ]
[ 98304 = {\left(4+4\right)}^{4}\times4! ]
[ 98306 = \sqrt{4}+\left(4!\times{\sqrt{\sqrt{4}}}^{4!}\right) ]
[ 98308 = \left(4!\times{\sqrt{\sqrt{4}}}^{4!}\right)+4 ]
[ 98320 = 4!\times\left({\sqrt{\sqrt{4}}}^{4!}+\sqrt{.\dot{4}}\right) ]
[ 98328 = 4!+\left(4!\times{\sqrt{\sqrt{4}}}^{4!}\right) ]
[ 98352 = 4!\times\left(\sqrt{4}+{\sqrt{\sqrt{4}}}^{4!}\right) ]
[ 98400 = 4!\times\left({\sqrt{\sqrt{4}}}^{4!}+4\right) ]
[ 98880 = 4!\times\left(4!+{\sqrt{\sqrt{4}}}^{4!}\right) ]
[ 100000 = {\frac{4}{.4}}^{\frac{\sqrt{4}}{.4}} ]

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