Powers n such that the sum of the digits in 3^n sets a record.
0, 1, 2, 6, 9, 14, 23, 25, 27, 34, 43, 47, 50, 62, 67, 71, 79, 82, 90, 98, 102, 112, 118, 122, 123, 139, 146, 154, 164, 166, 177, 179, 194, 200, 203, 205, 220, 230, 234, 243, 245, 258, 271, 287, 288, 317, 337, 349, 360, 369, 374, 376, 389, 410, 438, 448
1
The number 3^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[3^n]]; If[s > mx, mx = s; AppendTo[t, n]]; n++]; t
Cf. A004166 (sum of digits of 3^n), S000875-S000882.
nonn,base
T. D. Noe, May 11 2016