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A394057

Conjectured least positive integer k such that n^k has the largest average of digits and k>1.

2, 3, 2, 18, 10, 5, 2, 11, 7, 2, 9, 6, 14, 10, 11, 9, 2, 5, 3, 3, 18, 7, 11, 2, 5, 2, 9, 2, 15, 2, 12, 15, 12, 8, 9, 3, 5, 12, 13, 16, 3, 8, 3, 12, 129, 6, 4, 20, 14, 10, 19, 16, 3, 29, 17, 4, 7, 5, 9, 5, 90, 15, 2, 6, 34, 3, 2, 6, 13, 2, 59, 9, 9, 4, 9

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OFFSET

1,1

COMMENTS

All terms have been verified up to k <= 20000.

For n <= 47700, the largest term is a(10001) = 293.

LINKS

James C. McMahon, Table of n, a(n) for n = 1..1000

EXAMPLE

a(4) = 18, because 4^18 = 68719476736, which has the largest average of digits of ~5.82 for any 4^k and 1 < k <= 20000.

MATHEMATICA

a[n_]:=Module[{s=DigitSum[#]/IntegerLength[#]&/@(n^Range[2, 500])}, SequencePosition[s, {Max[s]}][[1, 1]]]+1; Array[a, 75] (* Increase range of k of n^k when for n>47700 *) (* James C. McMahon, Mar 20 2026 *)

CROSSREFS

Cf. A394058.

Sequence in context: A104507 A101033 A136454 * A025522 A350622 A019228

Adjacent sequences: A394054 A394055 A394056 * A394058 A394059 A394060

KEYWORD

nonn,base

AUTHOR

Dmitry Kamenetsky, Mar 09 2026

EXTENSIONS

a(42) corrected by James C. McMahon, Mar 20 2026

STATUS

approved

URL: https://oeis.org/A394057

⇱ A394057 - OEIS