A307498 Numbers k such that the digits of k in base 10 are a permutation of those of k in some other base.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 21, 23, 31, 41, 42, 43, 46, 51, 53, 61, 62, 63, 71, 73, 81, 82, 83, 84, 86, 91, 93, 158, 191, 196, 227, 261, 265, 283, 316, 370, 371, 441, 445, 511, 518, 551, 774, 782, 825, 834, 882, 910, 911, 912, 913, 914, 915, 916, 917, 918

Offset

1,3

Comments

Supersequence of A034294 and subsequence of A307498.

If the digits of k in base 10 is a permutation of m = (k in base b), 10^j < k < 10^(j+1), then 10^(j/(j+1)) < b < 10^((j+1)/j).

If k > 10, other base can only be 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 25, 26, 28, 37, 46, 55, 64, 73, 82.

The digits of k in base 10 is a permutation of k in base 82 iff k = 91.

The largest term is less than 10^25. See proof in A034294.

Links

Table of n, a(n) for n=1..61.

Example

13 in base 4 is 31, 227 in base 9 is 272.

Prog

(PARI) isok(k) = {my(v = vecsort(digits(k))); k < 10 || sum(j = 3, 82, vecsort(digits(k, j)) == v) > 1; }

Crossrefs

Cf. A034294, A115920, A308493.

Sequence in context: A075776 A261556 A033088 * A034294 A304246 A271837

Adjacent sequences: A307495 A307496 A307497 * A307499 A307500 A307501

Keyword

nonn,base,fini

Author

Jinyuan Wang, Aug 05 2019

Status

approved