Deadfish/Constants
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Given below are the shortest ways to produce a number in the range of 0 to 289 with Deadfish. At most 38 instructions are necessary to reach from 0 to any number in that range.
The shortest way to reach any number is to generate the instructions from right to left by adding i/ds from the nearest square, add an s, then continue isolating recursively until 0 to 3 are reached, which are then generated via is alone. 3 is included since it would otherwise be generated as iisd - its nearest square is 4.
For example, the code for 33 generates as such:
<code for 33>
<code for 36>ddd nearest square
<code for 6>sddd square root
<code for 4>iisddd nearest square
<code for 2>siisddd square root
iisiisddd ii
For numbers above 240, we theorize the same method holds, except for a couple caveats:
- The nearest valid square in the range 241 to 272 is no longer 256. Numbers below would lead to 225 = 15², and numbers above would lead to 289 = 17².
- Any squares involving 256 should be avoided.
- 65537 = 256² + 1 needs to go via 255² rather than 257² - they're the same distance, but the former is itself shorter.
List of Deadfish constants
0 = 1 = i 2 = ii 3 = iii 4 = iis 5 = iisi 6 = iisii 7 = iiisdd 8 = iiisd 9 = iiis 10 = iiisi 11 = iiisii 12 = iiisiii 13 = iissddd 14 = iissdd 15 = iissd 16 = iiss 17 = iissi 18 = iissii 19 = iissiii 20 = iissiiii 21 = iisisdddd 22 = iisisddd 23 = iisisdd 24 = iisisd 25 = iisis 26 = iisisi 27 = iisisii 28 = iisisiii 29 = iisisiiii 30 = iisisiiiii 31 = iisiisddddd 32 = iisiisdddd 33 = iisiisddd 34 = iisiisdd 35 = iisiisd 36 = iisiis 37 = iisiisi 38 = iisiisii 39 = iisiisiii 40 = iisiisiiii 41 = iisiisiiiii 42 = iisiisiiiiii 43 = iiisddsdddddd 44 = iiisddsddddd 45 = iiisddsdddd 46 = iiisddsddd 47 = iiisddsdd 48 = iiisddsd 49 = iiisdds 50 = iiisddsi 51 = iiisddsii 52 = iiisddsiii 53 = iiisddsiiii 54 = iiisddsiiiii 55 = iiisddsiiiiii 56 = iiisddsiiiiiii 57 = iiisdsddddddd 58 = iiisdsdddddd 59 = iiisdsddddd 60 = iiisdsdddd 61 = iiisdsddd 62 = iiisdsdd 63 = iiisdsd 64 = iiisds 65 = iiisdsi 66 = iiisdsii 67 = iiisdsiii 68 = iiisdsiiii 69 = iiisdsiiiii 70 = iiisdsiiiiii 71 = iiisdsiiiiiii 72 = iiisdsiiiiiiii 73 = iiissdddddddd 74 = iiissddddddd 75 = iiissdddddd 76 = iiissddddd 77 = iiissdddd 78 = iiissddd 79 = iiissdd 80 = iiissd 81 = iiiss 82 = iiissi 83 = iiissii 84 = iiissiii 85 = iiissiiii 86 = iiissiiiii 87 = iiissiiiiii 88 = iiissiiiiiii 89 = iiissiiiiiiii 90 = iiissiiiiiiiii 91 = iiisisddddddddd 92 = iiisisdddddddd 93 = iiisisddddddd 94 = iiisisdddddd 95 = iiisisddddd 96 = iiisisdddd 97 = iiisisddd 98 = iiisisdd 99 = iiisisd 100 = iiisis 101 = iiisisi 102 = iiisisii 103 = iiisisiii 104 = iiisisiiii 105 = iiisisiiiii 106 = iiisisiiiiii 107 = iiisisiiiiiii 108 = iiisisiiiiiiii 109 = iiisisiiiiiiiii 110 = iiisisiiiiiiiiii 111 = iiisiisdddddddddd 112 = iiisiisddddddddd 113 = iiisiisdddddddd 114 = iiisiisddddddd 115 = iiisiisdddddd 116 = iiisiisddddd 117 = iiisiisdddd 118 = iiisiisddd 119 = iiisiisdd 120 = iiisiisd 121 = iiisiis 122 = iiisiisi 123 = iiisiisii 124 = iiisiisiii 125 = iiisiisiiii 126 = iiisiisiiiii 127 = iiisiisiiiiii 128 = iiisiisiiiiiii 129 = iiisiisiiiiiiii 130 = iiisiisiiiiiiiii 131 = iiisiisiiiiiiiiii 132 = iiisiisiiiiiiiiiii 133 = iiisiiisddddddddddd 134 = iiisiiisdddddddddd 135 = iiisiiisddddddddd 136 = iiisiiisdddddddd 137 = iiisiiisddddddd 138 = iiisiiisdddddd 139 = iiisiiisddddd 140 = iiisiiisdddd 141 = iiisiiisddd 142 = iiisiiisdd 143 = iiisiiisd 144 = iiisiiis 145 = iiisiiisi 146 = iiisiiisii 147 = iiisiiisiii 148 = iiisiiisiiii 149 = iiisiiisiiiii 150 = iiisiiisiiiiii 151 = iiisiiisiiiiiii 152 = iiisiiisiiiiiiii 153 = iiisiiisiiiiiiiii 154 = iiisiiisiiiiiiiiii 155 = iiisiiisiiiiiiiiiii 156 = iiisiiisiiiiiiiiiiii 157 = iissdddsdddddddddddd 158 = iissdddsddddddddddd 159 = iissdddsdddddddddd 160 = iissdddsddddddddd 161 = iissdddsdddddddd 162 = iissdddsddddddd 163 = iissdddsdddddd 164 = iissdddsddddd 165 = iissdddsdddd 166 = iissdddsddd 167 = iissdddsdd 168 = iissdddsd 169 = iissddds 170 = iissdddsi 171 = iissdddsii 172 = iissdddsiii 173 = iissdddsiiii 174 = iissdddsiiiii 175 = iissdddsiiiiii 176 = iissdddsiiiiiii 177 = iissdddsiiiiiiii 178 = iissdddsiiiiiiiii 179 = iissdddsiiiiiiiiii 180 = iissdddsiiiiiiiiiii 181 = iissdddsiiiiiiiiiiii 182 = iissdddsiiiiiiiiiiiii 183 = iissddsddddddddddddd 184 = iissddsdddddddddddd 185 = iissddsddddddddddd 186 = iissddsdddddddddd 187 = iissddsddddddddd 188 = iissddsdddddddd 189 = iissddsddddddd 190 = iissddsdddddd 191 = iissddsddddd 192 = iissddsdddd 193 = iissddsddd 194 = iissddsdd 195 = iissddsd 196 = iissdds 197 = iissddsi 198 = iissddsii 199 = iissddsiii 200 = iissddsiiii 201 = iissddsiiiii 202 = iissddsiiiiii 203 = iissddsiiiiiii 204 = iissddsiiiiiiii 205 = iissddsiiiiiiiii 206 = iissddsiiiiiiiiii 207 = iissddsiiiiiiiiiii 208 = iissddsiiiiiiiiiiii 209 = iissddsiiiiiiiiiiiii 210 = iissddsiiiiiiiiiiiiii 211 = iissdsdddddddddddddd 212 = iissdsddddddddddddd 213 = iissdsdddddddddddd 214 = iissdsddddddddddd 215 = iissdsdddddddddd 216 = iissdsddddddddd 217 = iissdsdddddddd 218 = iissdsddddddd 219 = iissdsdddddd 220 = iissdsddddd 221 = iissdsdddd 222 = iissdsddd 223 = iissdsdd 224 = iissdsd 225 = iissds 226 = iissdsi 227 = iissdsii 228 = iissdsiii 229 = iissdsiiii 230 = iissdsiiiii 231 = iissdsiiiiii 232 = iissdsiiiiiii 233 = iissdsiiiiiiii 234 = iissdsiiiiiiiii 235 = iissdsiiiiiiiiii 236 = iissdsiiiiiiiiiii 237 = iissdsiiiiiiiiiiii 238 = iissdsiiiiiiiiiiiii 239 = iissdsiiiiiiiiiiiiii 240 = iissdsiiiiiiiiiiiiiii 241 = iissdsiiiiiiiiiiiiiiii 242 = iissdsiiiiiiiiiiiiiiiii 243 = iissdsiiiiiiiiiiiiiiiiii 244 = iissdsiiiiiiiiiiiiiiiiiii 245 = iissdsiiiiiiiiiiiiiiiiiiii 246 = iissdsiiiiiiiiiiiiiiiiiiiii 247 = iissdsiiiiiiiiiiiiiiiiiiiiii 248 = iissdsiiiiiiiiiiiiiiiiiiiiiii 249 = iissdsiiiiiiiiiiiiiiiiiiiiiiii 250 = iissdsiiiiiiiiiiiiiiiiiiiiiiiii 251 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiii 252 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiiii 253 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiiiii 254 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiiiiii 255 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiiiiiii 257 = iissisdddddddddddddddddddddddddddddddd 258 = iissisddddddddddddddddddddddddddddddd 259 = iissisdddddddddddddddddddddddddddddd 260 = iissisddddddddddddddddddddddddddddd 261 = iissisdddddddddddddddddddddddddddd 262 = iissisddddddddddddddddddddddddddd 263 = iissisdddddddddddddddddddddddddd 264 = iissisddddddddddddddddddddddddd 265 = iissisdddddddddddddddddddddddd 266 = iissisddddddddddddddddddddddd 267 = iissisdddddddddddddddddddddd 268 = iissisddddddddddddddddddddd 269 = iissisdddddddddddddddddddd 270 = iissisddddddddddddddddddd 271 = iissisdddddddddddddddddd 272 = iissisddddddddddddddddd 273 = iissisdddddddddddddddd 274 = iissisddddddddddddddd 275 = iissisdddddddddddddd 276 = iissisddddddddddddd 277 = iissisdddddddddddd 278 = iissisddddddddddd 279 = iissisdddddddddd 280 = iissisddddddddd 281 = iissisdddddddd 282 = iissisddddddd 283 = iissisdddddd 284 = iissisddddd 285 = iissisdddd 286 = iissisddd 287 = iissisdd 288 = iissisd 289 = iissis 290 = iissisi