A334150 Primes p such that p AND q = 1, where q is the next prime after p and AND is the bitwise operation.

3, 13, 61, 251, 4093, 32749, 65521, 8388593, 33554393, 1073741789, 137438953447, 9007199254740881, 36028797018963913, 144115188075855859, 147573952589676412909, 37778931862957161709471, 75557863725914323419121, 2417851639229258349412301, 4835703278458516698824647

Offset: 1

Author

Michel Marcus, Apr 16 2020

Keywords

• nonn
• base

Crossrefs

Cf. A175330.

Subsequence of A014234 (largest prime <= 2^n).

Cf. A214415 (exponents of corresponding powers of 2).

Programs

Mathematica

s = {}; p = 2; Do[q = NextPrime[p]; If[BitAnd[p, q] == 1, AppendTo[s, p]]; p = q, {10^5}]; s (* Amiram Eldar, Apr 16 2020 *)
Select[ NextPrime[ 2^Range[82], -1], BitAnd[#, NextPrime@ #] == 1 &] (* Giovanni Resta, Apr 16 2020 *)

PARI

isok(p) = isprime(p) && (bitand(p, nextprime(p+1)) == 1);

Extensions

a(9)-a(10) from Amiram Eldar, Apr 16 2020

a(11)-a(19) from Giovanni Resta, Apr 16 2020