A217163 a(n) is the least value of k such that the decimal expansion of n^k contains eight or more consecutive identical digits.

8554, 7720, 4277, 2790, 8533, 6176, 4442, 3860, 8, 2983, 2430, 5482, 1053, 5030, 3502, 5781, 3982, 4706, 8, 2568, 4850, 2740, 4549, 1395, 699, 2960, 2679, 3197, 8, 4057, 2709, 3115, 3436, 1190, 6629, 692, 3274, 5773, 8, 6997, 3536, 5936, 647, 3204, 1369, 1587

Offset: 2

Author

V. Raman, Sep 27 2012

Keywords

• nonn
• base

Links

• V. Raman, Table of n, a(n) for n = 2..100

Crossrefs

Cf. A045875, A215727, A215728, A215729, A215730, A215731.

Programs

Mathematica

Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 7, 1], {0, 0, 0, 0, 0, 0, 0}], k++]; k, {n, 2, 50}] (* T. D. Noe, Oct 01 2012 *)
lvk8[n_]:=Module[{k=Ceiling[Log[n,11111111]]},While[Max[Length/@ Split[ IntegerDigits[n^k]]]<8,k++];k] Array[lvk8, 50, 2] (* Harvey P. Dale, Jul 31 2013 *)

Extensions

Definition clarified by Harvey P. Dale, Jul 31 2013