Numbers n such that 2^n is in S000906.
1, 18, 22, 23, 24, 36, 39, 45, 46, 51, 54, 59, 62, 63, 66, 70, 71, 78, 81, 88, 90, 94, 102, 108, 111, 114, 115, 116, 117, 119, 126, 135, 138, 142, 144, 150, 151, 153, 156, 162, 166, 170, 171, 174, 180, 182, 186, 190, 195, 198, 202, 206, 207, 214, 216, 219
1
This sequence is relatively easy to compute because only powers of 2 are involved.
T. D. Noe, Plot of 56 terms
(Mma) s = Table[Or @@ PrimeQ /@ Total /@ Union[Sort /@ Flatten[Table[2^a, {a, Compositions[i, 3]}], 0]], {i, 200}]; Flatten[Position[s, False]]
nonn
T. D. Noe, Jun 15 2016