A215236 Greatest integer k such that n^i has no identical consecutive digits for i = 0..k.

15, 10, 7, 10, 4, 5, 5, 5, 1, 0, 1, 8, 2, 1, 3, 6, 4, 4, 1, 1, 0, 5, 3, 5, 4, 3, 7, 4, 1, 5, 4, 0, 1, 1, 2, 6, 1, 3, 1, 4, 2, 3, 0, 2, 1, 1, 2, 2, 1, 6, 3, 2, 5, 0, 3, 3, 1, 3, 1, 2, 1, 2, 2, 1, 0, 1, 2, 3, 1, 2, 6, 5, 2, 5, 1, 0, 2, 3, 1, 2, 2, 1, 4, 1, 3, 5, 0

Offset: 2

Author

T. D. Noe, Sep 17 2012

Keywords

• nonn
• base

Examples

			a(2) = 15 because the powers of 2 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536 and only the 16th power has consecutive identical digits.
		

Links

• T. D. Noe, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A216063 (highest power of n having different consecutive digits), A217157.

Programs

Mathematica

Table[k = 1; While[! MemberQ[Differences[IntegerDigits[n^k]], 0], k++]; k = k - 1, {n, 2, 100}]

Formula

a(n) = A217157(n) - 1. - Georg Fischer, Nov 25 2020