Powers n such that the sum of the digits in 4^n sets a record.
0, 1, 2, 3, 4, 6, 7, 8, 10, 12, 13, 14, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 32, 33, 37, 46, 47, 56, 58, 59, 60, 62, 65, 70, 71, 74, 75, 76, 83, 86, 89, 92, 93, 107, 110, 115, 120, 128, 134, 141, 150, 154, 155, 156, 158, 163, 164, 166, 167, 171, 172, 193
1
The number 4^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[4^n]]; If[s > mx, mx = s; AppendTo[t, n]]; n++]; t
Cf. A065713 (sum of digits of 4^n), S000875-S000882.
nonn,base
T. D. Noe, May 11 2016