%I #13 Nov 10 2022 11:39:32
%S 8,16,8,35,4,27,8,16,4,9,19,28,17,28,8,15,8,12,4,15,10,21,20,35,16,16,
%T 15,8,5,11,13,16,16,28,15,24,4,20,5,23,7,12,20,30,20,14,29,29,6,26,18,
%U 13,20,44,42,15,20,18,6,25,20,33,8,13,17,24,13,23,6,21
%N a(n) is the number of digits in the decimal representation of the smallest power of n that contains three consecutive identical digits.
%C Number of digits in n^k is equal to floor(1 + k*log_10(n)).
%H V. Raman, <a href="/A217178/b217178.txt">Table of n, a(n) for n = 2..10000</a>
%t Table[k = 1; While[d = IntegerDigits[n^k]; ! MemberQ[Partition[Differences[d], 2, 1], {0, 0}], k++]; Length[d], {n, 2, 100}] (* _T. D. Noe_, Oct 03 2012 *)
%t spn3[n_]:=Module[{p=1},While[SequenceCount[IntegerDigits[n^p],{x_,x_,x_}]<1,p++];IntegerLength[n^p]]; Array[spn3,80,2] (* _Harvey P. Dale_, Nov 10 2022 *)
%Y Cf. A217158, A217168.
%K nonn,base
%O 2,1
%A _V. Raman_, Sep 27 2012