A332535 Numbers that are not of the form p + 2^(2^k) + 2^q with p, q primes and k >= 0.

1, 2, 3, 4, 5, 6, 7, 16, 18, 20, 24, 28, 30, 32, 34, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 136, 138

Offset: 1

Author

N. J. A. Sloane, Feb 15 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Christian Elsholtz, Florian Luca, and Stefan Planitzer, Romanov type problems, The Ramanujan Journal 47.2 (2018): 267-289.

Crossrefs

Cf. A218044, A332379, A332534.

Programs

Maple

q:= proc(n) local k, i;
      for k from 0 while 2^(2^k)Alois P. Heinz, Feb 15 2020

Mathematica

q[n_] := Module[{k, i}, For[k = 0 , 2^(2^k) < n, k++, For[i = 1, 2^(2^k) + 2^Prime[i] < n, i++, If[PrimeQ[n - 2^(2^k) - 2^Prime[i]], Return[False]]] ]; True];
Select[Range[200], q] (* Jean-François Alcover, Nov 27 2020, after Alois P. Heinz *)