Irregular triangle of numbers n such that 2^n does not contain 0, 1, …, 9.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 18, 19, 24, 25, 27, 28, 31, 32, 33, 34, 35, 36, 37, 39, 49, 51, 67, 72, 76, 77, 81, 86, 1, 2, 3, 5, 6, 8, 11, 12, 15, 16, 19, 23, 25, 28, 32, 33, 35, 38, 43, 52, 56, 59, 63, 66, 73, 91, 0, 2, 3, 4, 6, 12, 14, 16

1

The irregular triangle has 10 rows of different lengths.

T. D. Noe, Plot of 298 terms

T. D. Noe, Table of 298 terms

(Mma) k = 2; t = {}; Do[s = Position[Reverse[IntegerDigits[k^n]], i]; If[Length[s] == 0, AppendTo[t, n]], {i, 0, 9}, {n, 0, 1000}]; t

nonn,base,tabf

T. D. Noe, Oct 14 2014