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A217181 a(n) is the number of digits in the decimal representation of the smallest power of n that contains six consecutive identical digits. 1

%I

%S 293,257,293,760,289,148,293,257,7,502,391,365,225,607,293,431,362,

%T 185,8,1184,1104,325,664,1590,398,258,184,524,9,427,684,435,532,170,

%U 749,543,497,713,10,912,630,450,148,1029,385,755,63,432,11,822,347,330,818,537

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

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

%H V. Raman, <a href="/A217181/b217181.txt">Table of n, a(n) for n = 2..10000</a>

%t Table[k = 1; While[d = IntegerDigits[n^k]; ! MemberQ[Partition[Differences[d], 5, 1], {0, 0, 0, 0, 0}], k++]; Length[d], {n, 2, 100}] (* _T. D. Noe_, Oct 03 2012 *)

%t spn6[n_]:=Module[{k=1},While[SequenceCount[IntegerDigits[n^k],{x_,x_,x_,x_,x_,x_}]< 1,k++];IntegerLength[n^k]]; Array[spn6,55,2] (* _Harvey P. Dale_, Jun 21 2022 *)

%Y Cf. A217161, A217171.

%K nonn,base

%O 2,1

%A _V. Raman_, Sep 27 2012

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Last modified February 3 21:17 EST 2023. Contains 360045 sequences. (Running on oeis4.)