Powers n such that the sum of the digits in 2^n sets a record.
0, 1, 2, 3, 6, 7, 8, 11, 12, 13, 14, 15, 19, 20, 23, 28, 31, 32, 33, 36, 38, 39, 48, 50, 51, 54, 55, 66, 67, 74, 91, 94, 112, 115, 116, 118, 120, 121, 124, 129, 130, 131, 139, 141, 148, 150, 151, 152, 157, 165, 172, 175, 185, 213, 220, 230, 240, 255, 267, 282
1
The number 2^n is computed in base 10.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Power of 2
(Mma) nn = 60; mx = -1; t = {}; n = 0; While[Length[t] < nn, s = Total[IntegerDigits[2^n]]; If[s > mx, mx = s; AppendTo[t, n]]; n++]; t
Cf. A001370 (sum of digits of 2^n), S000876-S000882.
nonn,base
T. D. Noe, May 11 2016