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

1,1

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.

Links

Table of n, a(n) for n=1..57.

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 *)

Crossrefs

Cf. A000079, A061345.

Cf. A006512, A053703, A115231, A115233.

Sequence in context: A175212 A066047 A240710 * A332346 A020626 A136207

Adjacent sequences: A115229 A115230 A115231 * A115233 A115234 A115235

Keyword

nonn

Author

Reinhard Zumkeller, Jan 17 2006

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

Status

approved