A217179 a(n) is the number of digits in the decimal representation of the smallest power of n that contains four consecutive identical digits.

13, 16, 55, 67, 90, 61, 55, 84, 5, 41, 20, 28, 17, 116, 55, 64, 98, 90, 6, 39, 57, 48, 57, 68, 63, 16, 31, 55, 6, 27, 55, 108, 53, 28, 100, 32, 62, 51, 7, 65, 33, 33, 74, 55, 55, 24, 61, 68, 7, 64, 73, 51, 68, 110, 42, 18, 46, 18, 8, 115, 27, 54, 55, 33, 31, 106

Offset

2,1

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

Mathematica

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 *)
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 *)

Crossrefs

Cf. A217159, A217169.

Sequence in context: A056663 A274978 A103230 * A107081 A029526 A219949

Adjacent sequences: A217176 A217177 A217178 * A217180 A217181 A217182

Keyword

nonn,base

Author

V. Raman, Sep 27 2012

Status

approved