A217161 -id:A217161 - cp's OEIS frontend

A217171 a(n) is the first digit (from the left) to appear six times in succession in the decimal representation n^A217161(n).

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

Offset: 2

V. Raman, Sep 27 2012

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

Cf. A217161.

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

Table[k = 1; While[d = IntegerDigits[n^k]; df = Partition[Differences[d], 5, 1]; ! MemberQ[df, {0, 0, 0, 0, 0}], k++]; d[[Position[df, {0, 0, 0, 0, 0}][[1, 1]]]], {n, 2, 100}] (* T. D. Noe, Oct 02 2012 *)

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

Original entry on oeis.org

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

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. A217161, A217171.

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 *)

cp's OEIS Frontend

A217171 a(n) is the first digit (from the left) to appear six times in succession in the decimal representation n^A217161(n).

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