A240069 The number n^k has all 10 decimal digits starting at k = a(n), or a(n) = 0 if 10 digits are not possible.

0, 169, 107, 85, 66, 65, 62, 57, 54, 0, 42, 52, 38, 35, 35, 43, 28, 26, 45, 169, 30, 25, 51, 24, 30, 32, 29, 29, 46, 107, 29, 19, 25, 35, 19, 33, 26, 18, 42, 85, 24, 20, 21, 30, 40, 33, 16, 30, 17, 66, 30, 30, 31, 19, 18, 34, 20, 32, 28, 65, 27, 20, 25, 29, 18, 16

Offset: 1

Author

T. D. Noe, Apr 01 2014

Keywords

• nonn
• base

Comments

It appears that numbers of the form 2 * 10^i have the longest period, 169.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A137214 (number of distinct decimal digits in 2^n).

Programs

Mathematica

mx = 1000; Table[s = Table[Length[Union[IntegerDigits[n^k]]], {k, 0, mx}]; pos = Position[s, 10]; If[pos == {}, 0, 1 + mx - Position[Differences[Reverse[s]], _?(# != 0 &)][[1, 1]]], {n, 100}]