

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.


1



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
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OFFSET

1,2


COMMENTS

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


LINKS



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).


KEYWORD

nonn,base


AUTHOR



STATUS

approved



