A217179 - OEIS

A217179

a(n) is the number of digits in the decimal representation of the smallest power of n that contains four consecutive identical digits.

%I #13 Jul 01 2021 17:45:17

%S 13,16,55,67,90,61,55,84,5,41,20,28,17,116,55,64,98,90,6,39,57,48,57,

%T 68,63,16,31,55,6,27,55,108,53,28,100,32,62,51,7,65,33,33,74,55,55,24,

%U 61,68,7,64,73,51,68,110,42,18,46,18,8,115,27,54,55,33,31,106

%N a(n) is the number of digits in the decimal representation of the smallest power of n that contains four consecutive identical digits.

%C Number of digits in n^k is equal to floor(1 + k*log_10(n)).

%H V. Raman, <a href="/A217179/b217179.txt">Table of n, a(n) for n = 2..10000</a>

%t Table[k = 1; While[d = IntegerDigits[n^k]; ! MemberQ[Partition[Differences[d], 3, 1], {0, 0, 0}], k++]; Length[d], {n, 2, 100}] (* _T. D. Noe_, Oct 03 2012 *)

%t ndsp[n_]:=Module[{k=1},While[SequenceCount[IntegerDigits[n^k],{x_,x_,x_,x_}] <1,k++];IntegerLength[n^k]]; Array[ndsp,70,2] (* _Harvey P. Dale_, Jul 01 2021 *)

%Y Cf. A217159, A217169.

%K nonn,base

%O 2,1

%A _V. Raman_, Sep 27 2012