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

1,2

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

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}]

Crossrefs

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

Sequence in context: A297048 A003929 A343269 * A184035 A044869 A260055

Adjacent sequences: A240066 A240067 A240068 * A240070 A240071 A240072

Keyword

nonn,base

Author

T. D. Noe, Apr 01 2014

Status

approved