A217163 - OEIS

A217163

a(n) is the least value of k such that the decimal expansion of n^k contains eight or more consecutive identical digits.

%I #14 Jul 31 2013 16:16:49

%S 8554,7720,4277,2790,8533,6176,4442,3860,8,2983,2430,5482,1053,5030,

%T 3502,5781,3982,4706,8,2568,4850,2740,4549,1395,699,2960,2679,3197,8,

%U 4057,2709,3115,3436,1190,6629,692,3274,5773,8,6997,3536,5936,647,3204,1369,1587

%N a(n) is the least value of k such that the decimal expansion of n^k contains eight or more consecutive identical digits.

%H V. Raman, <a href="/A217163/b217163.txt">Table of n, a(n) for n = 2..100</a>

%t Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 7, 1], {0, 0, 0, 0, 0, 0, 0}], k++]; k, {n, 2, 50}] (* _T. D. Noe_, Oct 01 2012 *)

%t lvk8[n_]:=Module[{k=Ceiling[Log[n,11111111]]},While[Max[Length/@ Split[ IntegerDigits[n^k]]]<8,k++];k] Array[lvk8, 50, 2] (* _Harvey P. Dale_, Jul 31 2013 *)

%Y Cf. A045875, A215727, A215728, A215729, A215730, A215731.

%K nonn,base

%O 2,1

%A _V. Raman_, Sep 27 2012

%E Definition clarified by _Harvey P. Dale_, Jul 31 2013