Powers n such that the sum of the digits in 6^n sets a record.
0, 1, 2, 4, 5, 7, 11, 14, 15, 17, 21, 24, 26, 29, 39, 40, 46, 51, 59, 60, 64, 65, 71, 75, 77, 83, 90, 104, 106, 107, 114, 117, 121, 130, 133, 134, 141, 146, 158, 163, 164, 167, 180, 186, 188, 192, 199, 207, 224, 238, 239, 249, 250, 254, 257, 271, 276, 282
1
The number 6^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[6^n]]; If[s > mx, mx = s; AppendTo[t, n]]; n++]; t
Cf. A066002 (sum of digits of 6^n), S000875-S000882.
nonn,base
T. D. Noe, May 11 2016