Powers n such that the sum of the digits in 5^n sets a record.
0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 15, 16, 18, 22, 23, 24, 27, 30, 31, 32, 36, 38, 39, 41, 42, 43, 44, 49, 55, 56, 57, 72, 73, 74, 75, 83, 90, 94, 96, 103, 105, 106, 111, 112, 113, 127, 128, 129, 134, 135, 138, 142, 149, 153, 154, 155, 156, 166, 175, 176, 177
1
The number 5^n is computed in base 10.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) nn = 60; mx = -1; t = {}; n = 0; While[Length[t] < nn, s = Total[IntegerDigits[5^n]]; If[s > mx, mx = s; AppendTo[t, n]]; n++]; t
Cf. A066001 (sum of digits of 5^n), S000875-S000882.
nonn,base
T. D. Noe, May 11 2016