5^a(n) is smallest power of 5 beginning with n^2.——OEIS就没有了。
0, 11, 10, 69, 2, 38, 104, 87, 183, 93, 209, 232, 69, 298, 434, 477, 231, 377, 915, 483, 1413, 403, 74, 2077, 4, 1233, 1007, 1947, 1432, 2083, 1764, 2611, 2488, 1395, 1953, 1541, 644, 913, 5454, 6889, 946, 1411,
Table, k = 0}, While, UpTo]] != t, k++]; k], {n, 49}]——众多个数字串可以共一个公式。
对数运算不一定快。譬如——A059449——a(n)! begins with 2^n.——1, 2, 8, 14, 89, 164, 18, 266, 304, 292, 2522, 557, 26438, 27045, 57134, 21936。
AbsoluteTiming] + 1]; k = 1; While] + 1]; a != (k! - Mod)/10^(c - b), k++]; Print, {n, 0, 15}]]——A059449——自带的公式。
{419.582, {1, 2, 8, 14, 89, 164, 18, 266, 304, 292, 2522, 557, 26438, 27045, 57134, 21936}}
AbsoluteTiming; k = 1; f = 1; While; If; If]];k++;]; k, {n, 0, 15}]]
{38.2066, {1, 2, 8, 14, 89, 164, 18, 266, 304, 292, 2522, 557, 26438, 27045, 57134, 21936}}
我这里出来就比A059449还要多了——{1, 2, 8, 14, 89, 164, 18, 266, 304, 292, 2522, 557, 26438, 27045, 57134, 21936, 224636, 529309}
OEIS——A387487——Numbers in the ring of integers Z such that k * k = k, the idempotents of Z.——0,1——最短的数字串！！！——"0"与"1"。
KEYWORD——nonn,bref,fini,full,nice,core,new——AUTHOR——Peter Luschny—— Aug 31 2025。
有见过这数字串的, 给个通项公式。 谢谢！！！
{0, 1, 2, 3, 4, 55, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1155, 16, 17, 18, 19, 20, 21, 22, 23, 24, 2255, 26, 27, 28, 29, 30, 31, 32, 33, 34, 3355, 36, 37, 38, 39, 40, 41, 42, 43, 44, 4455, 46, 47, 48, 49, 50, 51, 52, 53, 54, 5555, 56, 57, 58, 59, 60,
61, 62, 63, 64, 6655, 66, 67, 68, 69, 70, 71, 72, 73, 74, 7755, 76, 77, 78, 79, 80, 81, 82, 83, 84, 8855, 86, 87, 88, 89, 90, 91, 92, 93, 94, 9955, 96, 97, 98, 99, 100, 101, 102, 103, 104, 110055, 106, 107, 108, 109, 110, 111, 112, 113, 114,
111155, 116, 117, 118, 119, 120, 121, 122, 123, 124, 112255, 126, 127, 128, 129, 130, 131, 132, 133, 134, 113355, 136, 137, 138, 139, 140, 141, 142, 143, 144, 114455, 146, 147, 148, 149, 150, 151, 152, 153, 154, 115555, 156, 157, 158,