| Exponents n | |
|---|---|
| b=2 | 0, 1, 2, 3, 4, ... |
| b=4 | Please see under b=2 |
| b=6 | 0, 1, 2, ... |
| b=8 | Impossible since 8=2^3 |
| b=10 | 0, 1, ... |
| b=12 | 0, ... |
| b=14 | 1, ... |
| b=16 | Please see under b=2 |
| b=18 | 0, ... |
| b=20 | 1, 2, ... |
| b=22 | 0, ... |
| b=24 | 1, 2, ... |
| b=26 | 1, ... |
| b=28 | 0, 2, ... |
| b=30 | 0, 5, ... |
| b=32 | Impossible since 32=2^5 |
| b=34 | 2, ... |
| b=36 | Please see under b=6 |
| b=38 | ... |
| b=40 | 0, 1, ... |
| b=42 | 0, ... |
| b=44 | 4, ... |
| b=46 | 0, 2, 9, ... |
| b=48 | 2, ... |
| b=50 | ... |
| b=52 | 0, ... |
| b=54 | 1, 2, 5, ... |
| b=56 | 1, 2, ... |
| b=58 | 0, ... |
| b=60 | 0, ... |
| b=62 | ... |
| b=64 | Impossible since 64=4^3 |
| b=66 | 0, 1, ... |
| b=68 | ... |
| b=70 | 0, ... |
| b=72 | 0, ... |
| b=74 | 1, 2, 4, ... |
| b=76 | 4, ... |
| b=78 | 0, ... |
| b=80 | 2, ... |
| b=82 | 0, 2, ... |
| b=84 | 1, ... |
| b=86 | ... |
| b=88 | 0, 2, ... |
| b=90 | 1, 2, ... |
| b=92 | ... |
| b=94 | 1, 4, ... |
| b=96 | 0, 5, ... |
| b=98 | ... |
| b=100 | Please see under b=10 |
| b=102 | 0, 6, ... |
| b=104 | ... |
| b=106 | 0, 2, ... |
| b=108 | 0, ... |
| b=110 | 1, ... |
| b=112 | 0, 5, ... |
| b=114 | 5, ... |
| b=116 | 1, ... |
| b=118 | 2, 3, ... |
| b=120 | 1, 7, ... |
| b=122 | ... |
| b=124 | 1, ... |
| b=126 | 0, 1, ... |
| b=128 | Impossible since 128=2^7 |
| b=130 | 0, 1, ... |
| b=132 | 2, 3, 5, ... |
| b=134 | 1, ... |
| b=136 | 0, ... |
| b=138 | 0, ... |
| b=140 | 2, 3, ... |
| b=142 | 2, ... |
| b=144 | Please see under b=12 |
| b=146 | 1, ... |
| b=148 | 0, ... |
| b=150 | 0, 1, 11, ... |
| b=152 | 3, ... |
| b=154 | 2, ... |
| b=156 | 0, 1, 4, 5, ... |
| b=158 | 4, ... |
| b=160 | 1, 2, ... |
| b=162 | 0, 6, ... |
| b=164 | 2, ... |
| b=166 | 0, ... |
| b=168 | ... |
| b=170 | 1, ... |
| b=172 | 0, ... |
| b=174 | 2, ... |
| b=176 | 1, 4, ... |
| b=178 | 0, ... |
| b=180 | 0, 1, 2, ... |
| b=182 | ... |
| b=184 | 1, ... |
| b=186 | ... |
| b=188 | 4, ... |
| b=190 | 0, 7, ... |
| b=192 | 0, ... |
| b=194 | 2, ... |
| b=196 | Please see under b=14 |
| b=198 | 0, 2, 4, ... |
| b=200 | ... |
| b=202 | ... |
| b=204 | 1, 2, ... |
| b=206 | 1, ... |
| b=208 | 3, ... |
| b=210 | 0, 1, 2, ... |
| b=212 | ... |
| b=214 | ... |
| b=216 | Impossible since 216=6^3 |
| b=218 | ... |
| b=220 | 2, ... |
| b=222 | 0, ... |
| b=224 | 1, ... |
| b=226 | 0, ... |
| b=228 | 0, 2, ... |
| b=230 | 1, ... |
| b=232 | 0, ... |
| b=234 | 7, ... |
| b=236 | 1, ... |
| b=238 | 0, 2, ... |
| b=240 | 0, 1, 3, ... |
| b=242 | 2, 3, ... |
| b=244 | ... |
| b=246 | ... |
| b=248 | 2, 4, ... |
| b=250 | 0, 1, ... |
| b=252 | ... |
| b=254 | 2, ... |
| b=256 | Please see under b=2 |
| b=258 | ... |
| b=260 | 1, ... |
| b=262 | 0, ... |
| b=264 | 1, ... |
| b=266 | 2, ... |
| b=268 | 0, ... |
| b=270 | 0, 1, ... |
| b=272 | 2, ... |
| b=274 | 6, ... |
| b=276 | 0, 2, ... |
| b=278 | 2, 8, ... |
| b=280 | 0, 1, ... |
| b=282 | 0, ... |
| b=284 | 1, ... |
| b=286 | ... |
| b=288 | 2, 3, 4, ... |
| b=290 | 3, ... |
| b=292 | 0, ... |
| b=294 | ... |
| b=296 | 2, ... |
| b=298 | ... |
| b=300 | 1, 6, ... |
| b=302 | ... |
| b=304 | ... |
| b=306 | 0, 1, 3, 4, ... |
| b=308 | ... |
| b=310 | 0, ... |
| b=312 | 0, 2, ... |
| b=314 | 1, ... |
| b=316 | 0, ... |
| b=318 | 4, ... |
| b=320 | 2, ... |
| b=322 | ... |
| b=324 | Please see under b=18 |
| b=326 | 1, ... |
| b=328 | 2, ... |
| b=330 | 0, 4, ... |
| b=332 | 5, ... |
| b=334 | 2, ... |
| b=336 | 0, ... |
| b=338 | ... |
| b=340 | 1, 2, ... |
| b=342 | 5, ... |
| b=344 | ... |
| b=346 | 0, ... |
| b=348 | 0, 4, ... |
| b=350 | 1, ... |
| b=352 | 0, 2, ... |
| b=354 | ... |
| b=356 | ... |
| b=358 | 0, ... |
| b=360 | 5, ... |
| b=362 | ... |
| b=364 | 2, ... |
| b=366 | 0, ... |
| b=368 | ... |
| b=370 | 4, ... |
| b=372 | 0, ... |
| b=374 | 2, ... |
| b=376 | 5, ... |
| b=378 | 0, 3, ... |
| b=380 | ... |
| b=382 | 0, 4, ... |
| b=384 | 1, ... |
| b=386 | 1, ... |
| b=388 | 0, ... |
| b=390 | ... |
| b=392 | 3, ... |
| b=394 | ... |
| b=396 | 0, 1, 4, ... |
| b=398 | ... |
| b=400 | Please see under b=20 |
| b=402 | ... |
| b=404 | ... |
| b=406 | 1, ... |
| b=408 | 0, ... |
| b=410 | ... |
| b=412 | 6, ... |
| b=414 | 2, ... |
| b=416 | ... |
| b=418 | 0, ... |
| b=420 | 0, 1, ... |
| b=422 | ... |
| b=424 | ... |
| b=426 | 3, ... |
| b=428 | 5, ... |
| b=430 | 0, 1, 2, 5, ... |
| b=432 | 0, 5, ... |
| b=434 | 3, ... |
| b=436 | 1, 2, ... |
| b=438 | 0, ... |
| b=440 | 1, ... |
| b=442 | 0, 2, 3, ... |
| b=444 | 1, ... |
| b=446 | ... |
| b=448 | 0, 5, ... |
| b=450 | ... |
| b=452 | 4, ... |
| b=454 | ... |
| b=456 | 0, 4, ... |
| b=458 | ... |
| b=460 | 0, ... |
| b=462 | 0, ... |
| b=464 | 1, ... |
| b=466 | 0, 1, 2, ... |
| b=468 | ... |
| b=470 | 1, 4, ... |
| b=472 | 2, ... |
| b=474 | 1, 4, ... |
| b=476 | 2, 4, ... |
| b=478 | 0, 4, ... |
| b=480 | ... |
| b=482 | ... |
| b=484 | Please see under b=22 |
| b=486 | 0, ... |
| b=488 | 2, ... |
| b=490 | 0, 1, ... |
| b=492 | 2, ... |
| b=494 | 2, ... |
| b=496 | 1, ... |
| b=498 | 0, 2, ... |
| b=500 | ... |
| b=502 | 0, ... |
| b=504 | 2, ... |
| b=506 | 7, ... |
| b=508 | 0, 3, ... |
| b=510 | 3, ... |
| b=512 | Impossible since 512=8^3 |
| b=514 | ... |
| b=516 | 2, ... |
| b=518 | ... |
| b=520 | 0, ... |
| b=522 | 0, ... |
| b=524 | ... |
| b=526 | 2, ... |
| b=528 | ... |
| b=530 | ... |
| b=532 | 7, ... |
| b=534 | ... |
| b=536 | 1, ... |
| b=538 | ... |
| b=540 | 0, 2, 3, ... |
| b=542 | 3, ... |
| b=544 | 1, ... |
| b=546 | 0, ... |
| b=548 | 7, ... |
| b=550 | 2, ... |
| b=552 | ... |
| b=554 | 2, ... |
| b=556 | 0, 1, 2, ... |
| b=558 | ... |
| b=560 | 4, ... |
| b=562 | 0, 3, 5, 6, ... |
| b=564 | ... |
| b=566 | 2, ... |
| b=568 | 0, 2, 4, ... |
| b=570 | 0, 1, ... |
| b=572 | ... |
| b=574 | ... |
| b=576 | Please see under b=24 |
| b=578 | ... |
| b=580 | ... |
| b=582 | 2, ... |
| b=584 | 1, 2, ... |
| b=586 | 0, ... |
| b=588 | 5, ... |
| b=590 | ... |
| b=592 | 0, 6, ... |
| b=594 | 1, ... |
| b=596 | 3, ... |
| b=598 | 0, 4, ... |
| b=600 | 0, 2, ... |
| b=602 | ... |
| b=604 | ... |
| b=606 | 0, ... |
| b=608 | ... |
| b=610 | 3, ... |
| b=612 | 0, ... |
| b=614 | 8, ... |
| b=616 | 0, 2, ... |
| b=618 | 0, ... |
| b=620 | ... |
| b=622 | ... |
| b=624 | 2, ... |
| b=626 | ... |
| b=628 | 2, ... |
| b=630 | 0, ... |
| b=632 | ... |
| b=634 | 1, ... |
| b=636 | 1, ... |
| b=638 | ... |
| b=640 | 0, ... |
| b=642 | 0, 4, ... |
| b=644 | 1, ... |
| b=646 | 0, 1, ... |
| b=648 | ... |
| b=650 | ... |
| b=652 | 0, ... |
| b=654 | 1, ... |
| b=656 | 2, ... |
| b=658 | 0, ... |
| b=660 | 0, ... |
| b=662 | ... |
| b=664 | 3, ... |
| b=666 | ... |
| b=668 | ... |
| b=670 | ... |
| b=672 | 0, ... |
| b=674 | 1, ... |
| b=676 | Please see under b=26 |
| b=678 | ... |
| b=680 | 1, 3, ... |
| b=682 | 0, 3, ... |
| b=684 | ... |
| b=686 | 1, 4, ... |
| b=688 | 4, ... |
| b=690 | 0, 1, 2, 4, ... |
| b=692 | ... |
| b=694 | ... |
| b=696 | 1, ... |
| b=698 | ... |
| b=700 | 0, 1, ... |
| b=702 | 2, ... |
| b=704 | 1, ... |
| b=706 | ... |
| b=708 | 0, ... |
| b=710 | 2, ... |
| b=712 | ... |
| b=714 | 1, ... |
| b=716 | 1, ... |
| b=718 | 0, ... |
| b=720 | ... |
| b=722 | ... |
| b=724 | ... |
| b=726 | 0, 5, ... |
| b=728 | 6, ... |
| b=730 | 2, ... |
| b=732 | 0, 2, 3, ... |
| b=734 | ... |
| b=736 | 4, ... |
| b=738 | 0, 2, 5, ... |
| b=740 | 1, ... |
| b=742 | 0, 2, ... |
| b=744 | ... |
| b=746 | ... |
| b=748 | 2, ... |
| b=750 | 0, 1, ... |
| b=752 | ... |
| b=754 | ... |
| b=756 | 0, ... |
| b=758 | 2, ... |
| b=760 | 0, 1, 2, ... |
| b=762 | ... |
| b=764 | 1, ... |
| b=766 | ... |
| b=768 | 0, 2, ... |
| b=770 | ... |
| b=772 | 0, 2, ... |
| b=774 | 4, ... |
| b=776 | 4, ... |
| b=778 | 2, 4, ... |
| b=780 | 1, ... |
| b=782 | 3, ... |
| b=784 | Please see under b=28 |
| b=786 | 0, 2, ... |
| b=788 | 2, ... |
| b=790 | 4, ... |
| b=792 | ... |
| b=794 | ... |
| b=796 | 0, ... |
| b=798 | 2, ... |
| b=800 | 2, 3, ... |
| b=802 | ... |
| b=804 | 5, ... |
| b=806 | ... |
| b=808 | 0, 3, ... |
| b=810 | 0, 2, ... |
| b=812 | ... |
| b=814 | ... |
| b=816 | 1, ... |
| b=818 | ... |
| b=820 | 0, ... |
| b=822 | 0, ... |
| b=824 | 10, ... |
| b=826 | 0, 1, ... |
| b=828 | 0, ... |
| b=830 | 4, ... |
| b=832 | 4, ... |
| b=834 | 4, ... |
| b=836 | ... |
| b=838 | 0, ... |
| b=840 | ... |
| b=842 | ... |
| b=844 | ... |
| b=846 | 4, ... |
| b=848 | ... |
| b=850 | 5, ... |
| b=852 | 0, ... |
| b=854 | ... |
| b=856 | 0, 2, ... |
| b=858 | 0, ... |
| b=860 | 1, ... |
| b=862 | 0, ... |
| b=864 | 1, ... |
| b=866 | 3, ... |
| b=868 | ... |
| b=870 | ... |
| b=872 | ... |
| b=874 | 2, ... |
| b=876 | 0, 3, ... |
| b=878 | ... |
| b=880 | 0, ... |
| b=882 | 0, ... |
| b=884 | 3, 5, ... |
| b=886 | 0, ... |
| b=888 | ... |
| b=890 | 1, ... |
| b=892 | 3, 8, ... |
| b=894 | 2, ... |
| b=896 | ... |
| b=898 | 8, ... |
| b=900 | Please see under b=30 |
| b=902 | ... |
| b=904 | ... |
| b=906 | 0, 1, ... |
| b=908 | ... |
| b=910 | 0, 1, ... |
| b=912 | 2, ... |
| b=914 | 2, ... |
| b=916 | 3, 4, ... |
| b=918 | 0, 3, ... |
| b=920 | 1, ... |
| b=922 | ... |
| b=924 | ... |
| b=926 | ... |
| b=928 | 0, 2, ... |
| b=930 | 1, 2, ... |
| b=932 | ... |
| b=934 | 3, ... |
| b=936 | 0, 1, 2, ... |
| b=938 | ... |
| b=940 | 0, ... |
| b=942 | ... |
| b=944 | ... |
| b=946 | 0, 1, 4, ... |
| b=948 | ... |
| b=950 | 1, ... |
| b=952 | 0, 2, ... |
| b=954 | ... |
| b=956 | 3, 4, ... |
| b=958 | ... |
| b=960 | 1, 7, ... |
| b=962 | 2, ... |
| b=964 | ... |
| b=966 | 0, 1, 2, ... |
| b=968 | ... |
| b=970 | 0, ... |
| b=972 | 4, ... |
| b=974 | ... |
| b=976 | 0, ... |
| b=978 | ... |
| b=980 | ... |
| b=982 | 0, 4, ... |
| b=984 | 4, ... |
| b=986 | 1, 2, ... |
| b=988 | ... |
| b=990 | 0, 3, ... |
| b=992 | 2, ... |
| b=994 | ... |
| b=996 | 0, 2, ... |
| b=998 | ... |
| b=1000 | Impossible since 1000=10^3 |
(Colored cells correspond to Sloane's A075090.)
Ellipsis (dots) means that no more terms are known. It does not necessarily imply that the sequence continues. One can conjecture that every row in the above table is a finite sequence.
There are several ways to define new integer sequences from the above table: Concatenate all rows. Or give number of terms in each row. Or list row numbers whose sequences are empty. None of these sequences appear in Sloane's. But since there may be terms not yet discovered in each row, it is probably best not to submit these sequences.
First b for which n occurs in the row: A056993
First b for which all of 0, 1, 2, ..., n occur in the row: A090872
| Currently known bases b | OEIS | ||
|---|---|---|---|
| n>22 | (none) | ||
| n=22 | 2^n=4194304 | (none) | |
| n=21 | 2^n=2097152 | 2524190 | |
| n=20 | 2^n=1048576 | 919444, 1059094, 1951734, 1963736, 3843236 | A321323 |
| n=19 | 2^n=524288 | 75898, 341112, 356926, 475856, 1880370, 2061748, 2312092, 2733014, 2788032, 2877652, and more | A243959 |
| n=18 | 2^n=262144 | 24518, 40734, 145310, 361658, 525094, 676754, 773620, 1415198, 1488256, 1615588, and more | A244150 |
| n=17 | 2^n=131072 | 62722, 130816, 228188, 386892, 572186, 689186, 909548, 1063730, 1176694, 1361244, and more | A253854 |
| n=16 | 2^n=65536 | 48594, 108368, 141146, 189590, 255694, 291726, 292550, 357868, 440846, 544118, and more | A251597 |
| n=15 | 2^n=32768 | 70906, 167176, 204462, 249830, 321164, 330716, 332554, 429370, 499310, 524552, and more | A226530 |
| n=14 | 2^n=16384 | 67234, 101830, 114024, 133858, 162192, 165306, 210714, 216968, 229310, 232798, and more | A226529 |
| n=13 | 2^n=8192 | 30406, 71852, 85654, 111850, 126308, 134492, 144642, 147942, 150152, 165894, and more | A226528 |
| n=12 | 2^n=4096 | 1534, 7316, 17582, 18224, 28234, 34954, 41336, 48824, 51558, 51914, and more | A088362 |
| n=11 | 2^n=2048 | 150, 2558, 4650, 4772, 11272, 13236, 15048, 23302, 26946, 29504, and more | A088361 |
| n=10 | 2^n=1024 | 824, 1476, 1632, 2462, 2484, 2520, 3064, 3402, 3820, 4026, and more | A057002 |
| n=9 | 2^n=512 | 46, 1036, 1318, 1342, 2472, 2926, 3154, 3878, 4386, 4464, and more | A057465 |
| n=8 | 2^n=256 | 278, 614, 892, 898, 1348, 1494, 1574, 1938, [2116], 2122, 2278, and more | A056995 |
| n=7 | 2^n=128 | 120, 190, 234, 506, 532, 548, 960, 1738, 1786, 2884, and more | A056994 |
| n=6 | 2^n=64 | 102, 162, 274, 300, 412, 562, 592, 728, 1084, 1094, and more | A006316 |
| n=5 | 2^n=32 | 30, 54, 96, 112, 114, 132, 156, 332, 342, 360, and more | A006315 |
| n=4 | 2^n=16 | 2, 44, 74, 76, 94, 156, 158, 176, 188, 198, and more | A006313 |
| n=3 | 2^n=8 | 2, [4], 118, 132, 140, 152, 208, 240, 242, 288, 290, and more | A006314 |
| n=2 | 2^n=4 | 2, [4], 6, [16], 20, 24, 28, 34, 46, 48, 54, 56, and more | A000068 |
| n=1 | 2^n=2 | 2, [4], 6, 10, 14, [16], 20, 24, 26, [36], 40, 54, 56, and more | A005574 |
| n=0 | 2^n=1 | 2, [4], 6, 10, 12, [16], 18, 22, 28, 30, [36], 40, 42, and more | A006093 |
In the above table, there is no guarantee the bases shown are the smallest possible.
See: