A217159 -id:A217159 - cp's OEIS frontend

A217169 a(n) is the first digit (from the left) to appear four times in succession in the decimal representation of n^A217159(n).

5, 5, 8, 7, 0, 9, 8, 5, 0, 7, 3, 6, 1, 2, 8, 9, 5, 1, 0, 4, 4, 7, 7, 8, 2, 5, 1, 0, 0, 9, 8, 6, 5, 5, 2, 6, 5, 6, 0, 9, 6, 7, 6, 5, 1, 6, 2, 2, 0, 6, 6, 3, 3, 1, 0, 3, 1, 1, 0, 7, 6, 2, 8, 3, 5, 9, 6, 8, 0, 1, 4, 8, 6, 3, 8, 1, 7, 9, 0, 5, 6, 9, 1, 2, 8, 1, 8

Offset: 2

V. Raman, Sep 27 2012

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

Cf. A217159.

Cf. A215732, A215733, A215734, A215735, A215736, A215737.

Table[k = 1; While[d = IntegerDigits[n^k]; df = Partition[Differences[d], 3, 1]; ! MemberQ[df, {0, 0, 0}], k++]; d[[Position[df, {0, 0, 0}][[1, 1]]]], {n, 2, 100}] (* T. D. Noe, Oct 02 2012 *)

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

Original entry on oeis.org

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

V. Raman, Sep 27 2012

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

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

Cf. A217159, A217169.

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 *)

cp's OEIS Frontend

A217169 a(n) is the first digit (from the left) to appear four times in succession in the decimal representation of n^A217159(n).

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