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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

%I #4 Apr 02 2014 03:29:13

%S 0,169,107,85,66,65,62,57,54,0,42,52,38,35,35,43,28,26,45,169,30,25,

%T 51,24,30,32,29,29,46,107,29,19,25,35,19,33,26,18,42,85,24,20,21,30,

%U 40,33,16,30,17,66,30,30,31,19,18,34,20,32,28,65,27,20,25,29,18,16

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

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

%H T. D. Noe, <a href="/A240069/b240069.txt">Table of n, a(n) for n = 1..1000</a>

%t 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}]

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

%K nonn,base

%O 1,2

%A _T. D. Noe_, Apr 01 2014

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