A307498 - OEIS

%I #32 Aug 26 2019 05:42:16

%S 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,

%T 82,83,84,86,91,93,158,191,196,227,261,265,283,316,370,371,441,445,

%U 511,518,551,774,782,825,834,882,910,911,912,913,914,915,916,917,918

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

%C Supersequence of A034294 and subsequence of A307498.

%C 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).

%C 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.

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

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

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

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

%Y Cf. A034294, A115920, A308493.

%K nonn,base,fini

%O 1,3

%A _Jinyuan Wang_, Aug 05 2019