For all k <= 16, Smallest n with G(n) = 2^k of 97 selected 3 place octal games and .6111... and Grundys Game Game | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 2^14 2^15 2^16 -----++------------------------------------------------------------------------------------------------------------------------------------- .004 | 5 9 21 76 158 509 1522 5895 22338 65759 157186 450547 1192770 _ _ _ _ .005 | 3 7 13 50 243 781 2452 7412 20186 61222 928227 _ _ _ _ _ _ .006 | 4 7 18 56 148 401 997 2168 4729 11143 36712 225569 902301 _ _ _ _ .007 | 3 6 15 55 154 434 1320 3217 9168 35662 109362 _ _ _ _ _ _ .014 | 2 8 13 83 385 845 2054 4295 11058 _ _ _ _ _ _ _ _ .015 | 2 7 14 77 463 1868 5526 _ _ _ _ _ _ _ _ _ _ .016 | 2 5 12 32 88 461 1896 9967 35745 116180 1136785 _ _ _ _ _ _ .024 |? 3 5 9 29 158 463 954 3366 12222 44424 262861 1438639 6837728 17881966 _ _ _ .026 |? 3 5 9 40 164 554 2028 5633 18998 39725 108472 287805 706590 2209569 8166576 26521820 _ .034 | 2 5 9 27 147 530 1441 4544 26376 _ _ _ _ _ _ _ _ .054 |P 2 5 9 40 130 3758 _ _ _ _ _ _ _ _ _ _ _ .055 |P 2 5 12 51 _ _ _ _ _ _ _ _ _ _ _ _ _ .06 |? 3 5 15 41 156 422 1036 3250 12542 31077 98963 361241 1186523 4160841 10847471 30808630 _ .064 | 3 5 9 27 76 238 904 1836 5758 62319 _ _ _ _ _ _ _ .104 |P 1 7 12 24 201 _ _ _ _ _ _ _ _ _ _ _ _ .106 |P 1 6 10 51 380 _ _ _ _ _ _ _ _ _ _ _ _ .114 | 1 7 13 58 284 1148 2949 6650 16636 16636 156339 _ _ _ _ _ _ .125 |? 1 3 17 64 390 1116 2523 5944 14222 39246 106704 299381 769278 1886477 4857184 11583695 29403456 .126 | 1 4 11 53 158 583 1271 3110 6845 14253 33116 109800 _ _ _ _ _ .127 |P 1 3 7 28 135 7646 _ _ _ _ _ _ _ _ _ _ _ .135 |? 1 3 17 64 340 1075 2895 6050 13999 36310 88759 328613 1138859 3573434 9110079 20492858 _ .136 |? 1 5 17 48 172 510 1692 3889 10644 29452 95009 298356 1069338 2834329 8858527 23069139 _ .14 | 1 6 12 54 1921 10793 89799 _ _ _ _ _ _ _ _ _ _ .142 | 1 4 13 33 187 456 946 2093 7440 _ _ _ _ _ _ _ _ .143 | 1 4 10 20 254 1483143 1890370 5129697 _ _ _ _ _ _ _ _ _ .146 | 1 4 7 28 86 273 841 1974 5305 14021 45111 _ _ _ _ _ _ .156 |P 1 4 7 29 243 _ _ _ _ _ _ _ _ _ _ _ _ .16 |P 1 5 8 161 1513 _ _ _ _ _ _ _ _ _ _ _ _ .161 | 1 3 13 63 399 863 1816 5011 _ _ _ _ _ _ _ _ _ .162 |? 1 4 10 31 101 355 1248 4568 19080 54963 185843 435867 1221964 2667917 5587200 12108248 28198223 .163 | 1 3 8 53 335 2438 19044 50822 127098 229695 469364 955245 1999571 4242293 9041647 20038874 _ .164 | 1 5 8 25 65 164 649 2099 6260 15831 38999 94438 189588 487235 1732287 _ _ .165 |P 1 3 9 17 117 _ _ _ _ _ _ _ _ _ _ _ _ .166 | 1 4 7 20 75 301 824 2376 _ _ _ _ _ _ _ _ _ .167 | 1 3 6 27 146 796 $1 _ _ _ _ _ _ _ _ _ _ .172 | 1 4 13 45 388 940 2456 4875 13458 _ _ _ _ _ _ _ _ .174 | 1 4 10 24 55 184 746 _ _ _ _ _ _ _ _ _ _ .204 | 2 5 18 65 183 453 1138 3664 12731 _ _ _ _ _ _ _ _ .205 | 2 3 15 45 120 485 2354052 _ _ _ _ _ _ _ _ _ _ .206 | 2 5 16 44 191 441 1108 3040 9813 29083 _ _ _ _ _ _ _ .207 | 2 3 11 28 152 420 1567 _ _ _ _ _ _ _ _ _ _ .224 | 2 3 12 56 202 449 1140 3059 11303 33931 133963 351183 1150935 2827463 7674449 _ _ .244 | 2 5 9 21 65 209 568 1492 4215 11886 31953 93412 259912 _ _ _ _ .245 | 2 3 7 17 53 189 446 1328 _ _ _ _ _ _ _ _ _ .264 | 2 3 5 13 47 156 348 906 2203 7279 _ _ _ _ _ _ _ .314 | 1 2 13 41 136 401 1059 4023 27070 100336 299411 848737 _ _ _ _ _ .324 | 1 3 9 34 139 397 1744 _ _ _ _ _ _ _ _ _ _ .334 | 1 2 13 33 167 364 1021 2143 5804 16482 68430 308875 1059155 2832965 8484694 28581365 _ .336 | 1 2 7 54 224 945 54117 _ _ _ _ _ _ _ _ _ _ .342 |? 1 4 13 46 259 572 1027 2719 7043 22240 100030 391813 1539861 5240028 13154838 27744841 _ .344 | 1 4 7 18 91 360 704 2414 6378 23694 82407 _ _ _ _ _ _ .346 |? 1 4 7 17 81 219 734 2171 5115 13716 27922 64881 148878 410353 1307377 3263349 11051963 .354 |P 1 2 6 25 62 159 399 _ _ _ _ _ _ _ _ _ _ .356 |P 1 2 7 15 62 _ _ _ _ _ _ _ _ _ _ _ _ .36 | 1 3 13 63 399 874 1918 4463 _ _ _ _ _ _ _ _ _ .362 | 1 3 5 33 304 3843 17285 8392915 _ _ _ _ _ _ _ _ _ .364 | 1 3 9 26 63 188 359 759 1769 4549 _ _ _ _ _ _ _ .366 | 1 3 5 15 53 185 433 966 2140 10370 _ _ _ _ _ _ _ .37 | 1 2 10 47 380 951 1944 4177 10343 _ _ _ _ _ _ _ _ .371 | 1 2 8 39 105 322 957 3029 10078 64890 261037 695385 1553345 4754393 14574651 _ _ .374 | 1 2 6 25 75 167 416 1085 _ _ _ _ _ _ _ _ _ .376 |P 1 2 7 21 57 169 623 1999 _ _ _ _ _ _ _ _ _ .404 | 3 5 9 21 94 167 635 1711 16174 _ _ _ _ _ _ _ _ .414 |? 2 5 8 28 75 181 402 939 2078 5447 17283 46492 146849 421665 1149013 2867298 7221140 .416 | 2 4 7 19 84 153 341 825 1928 5399 _ _ _ _ _ _ _ .444 | 3 5 9 20 83 255 509 1086 _ _ _ _ _ _ _ _ _ .45 |P 2 4 9 37 _ _ _ _ _ _ _ _ _ _ _ _ _ .454 |P 2 4 7 19 90 334 _ _ _ _ _ _ _ _ _ _ _ .56 |P 1 3 5 19 60 256 22778 _ _ _ _ _ _ _ _ _ _ .564 | 1 3 5 15 44 113 239 522 2780 6460 _ _ _ _ _ _ _ .6 | 2 3 11 48 381 952 1945 4178 10344 _ _ _ _ _ _ _ _ .604 |? 2 3 11 31 105 211 567 1601 3316 10586 34745 100785 281353 717266 1816792 4261897 9975103 .606 | 2 3 5 29 95 387 1004 2371 5674 15795 635867 _ _ _ _ _ _ .64 | 2 3 5 15 79 158 436 1128 3833 _ _ _ _ _ _ _ _ .644 |P 2 3 5 12 27 62 333 _ _ _ _ _ _ _ _ _ _ .74 | 1 4 7 19 50 242 704 1768 4757 $2 _ _ _ _ _ _ _ .744 | 1 4 7 16 50 110 277 661 1822 5757 _ _ _ _ _ _ _ .76 | 1 3 5 21 78 283 744 1875 4321 10621 30287 92182 249001 678472 2603917 _ _ .764 | 1 3 5 15 38 141 315 658 1336 3058 6488 14967 39229 _ _ _ _ .774 | 1 2 5 12 39 100 308 797 2700 _ _ _ _ _ _ _ _ .776 | 1 2 4 14 34 301 653 1362 2860 _ _ _ _ _ _ _ _ 4.44 | 2 3 5 15 35 302 654 1363 2861 _ _ _ _ _ _ _ _ 4.004| 2 5 10 27 95 229 596 1596 3689 9021 25285 _ _ _ _ _ _ 4.007| 2 3 7 13 79 198 508 1118 2401 9499 _ _ _ _ _ _ _ 4.026| 2 3 5 18 53 156 396 954 2497 7461 15049 43465 172575 707949 2669737 _ _ 4.044| 2 5 9 17 35 119 244 1477 _ _ _ _ _ _ _ _ _ 4.045| 2 3 7 13 38 86 306 _ _ _ _ _ _ _ _ _ _ 4.064|P 2 3 5 11 39 71 236 _ _ _ _ _ _ _ _ _ _ 4.324| 1 2 7 24 85 180 447 1298 654707 _ _ _ _ _ _ _ _ 4.327| 1 2 3 17 71 271 617 1292 2784 6272 13914 73107 _ _ _ _ _ 4.344|P 1 2 7 12 24 162 _ _ _ _ _ _ _ _ _ _ _ 4.364|P 1 2 7 25 62 620 _ _ _ _ _ _ _ _ _ _ _ 4.367| 1 2 3 17 64 255 1368 _ _ _ _ _ _ _ _ _ _ 4.404|P 2 3 6 21 50 162 332 1001 _ _ _ _ _ _ _ _ _ 4.406|P 2 3 5 10 29 74 _ _ _ _ _ _ _ _ _ _ _ Grund| 3 5 18 138 321 1056 4019 13133 7250049 _ _ _ _ _ _ _ _ .6111| 2 3 8 49 217 682 $3 _ _ _ _ _ _ _ _ _ _ -----++-------------------------------------------------------------------------------------------------------------------------------------- Game | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 2^14 2^15 2^16 $1 332129728 $2 76103606 $3 10397886 P preperiod and period length is known ? unknown sparse space structure --- last updated: 2021-04-28