A115232 Primes p which can be written in the form 2^i + q^j where i >= 0, j >= 1, q = odd prime.

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 1

Author

Reinhard Zumkeller, Jan 17 2006

Keywords

• nonn

Comments

a(n)=A000040(n+2) for n <= 32, but A000040(35)=149 is a term of A115231;

A115233 is a subsequence; the union with A115231 gives all primes (A000040);

A006512 and A053703 are subsequences.

Crossrefs

Cf. A000079, A061345.

Cf. A006512, A053703, A115231, A115233.

Programs

Mathematica

maxp = 281;
Union[Sort[Reap[Do[p = 2^i + q^j; If[p <= maxp && PrimeQ[p], Sow[p]], {i, 0, Log[2, maxp]//Ceiling}, {j, 1, Log[3, maxp]//Ceiling}, {q, Prime[Range[2, PrimePi[maxp]]]}]][[2, 1]]]] (* Jean-François Alcover, Aug 03 2018 *)

Extensions

Recomputed (based on recomputation of A115230) by R. J. Mathar and Reinhard Zumkeller, Apr 29 2010

Edited by N. J. A. Sloane, Apr 30 2010

Terms a(1)=2 and a(2)=3 removed from Data by Jean-François Alcover, Aug 03 2018