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

293, 257, 293, 760, 289, 148, 293, 257, 7, 502, 391, 365, 225, 607, 293, 431, 362, 185, 8, 1184, 1104, 325, 664, 1590, 398, 258, 184, 524, 9, 427, 684, 435, 532, 170, 749, 543, 497, 713, 10, 912, 630, 450, 148, 1029, 385, 755, 63, 432, 11, 822, 347, 330, 818, 537

Offset: 2

Author

V. Raman, Sep 27 2012

Keywords

• nonn
• base

Comments

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

Links

• V. Raman, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A217161, A217171.

Programs

Mathematica

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 *)
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 *)