A391816 a(n) is the smallest integer k >= 2 such that the decimal expansion of n is a subsequence of the decimal expansion of n^k.

2, 2, 5, 5, 3, 2, 2, 5, 5, 3, 2, 2, 3, 5, 7, 6, 5, 5, 5, 7, 5, 3, 4, 9, 3, 2, 8, 9, 5, 3, 5, 4, 3, 3, 3, 6, 6, 5, 5, 3, 3, 6, 9, 5, 5, 4, 4, 4, 5, 3, 2, 3, 7, 5, 3, 4, 3, 5, 5, 3, 2, 3, 5, 5, 3, 3, 6, 7, 5, 5, 5, 3, 3, 5, 7, 3, 2, 5, 5, 5, 5, 5, 5, 4, 5, 7, 4, 4

Offset

0,1

Links

Felix Huber, Table of n, a(n) for n = 0..10000

Example

a(4) = 3 since 4^3 = 64 and [4] is a subsequence of [6, 4] but not of [1, 6].

Maple

A391816 := proc(n) local k, m; m := convert(n, 'base', 10); for k from 2 do if ArrayTools:-IsSubsequence(m, convert(n^k, 'base', 10)) then return k; end if; end do; end proc: seq(A391816(n), n = 0 .. 87);

Crossrefs

Cf. A045537, A051248.

Sequence in context: A357123 A253600 A373203 * A045537 A243941 A161622

Adjacent sequences: A391813 A391814 A391815 * A391817 A391818 A391819

Keyword

base,nonn,easy

Author

Felix Huber, Jan 30 2026

Status

approved