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

Author

Jinyuan Wang, Aug 05 2019

Keywords

• nonn
• base
• fini

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.

Examples

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

Crossrefs

Cf. A034294, A115920, A308493.

Programs

PARI

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