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

1,1

Links

Table of n, a(n) for n=1..19.

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 *)

Prog

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

Crossrefs

Cf. A175330.

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

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

Sequence in context: A357749 A112568 A104089 * A239995 A319924 A108143

Adjacent sequences: A334147 A334148 A334149 * A334151 A334152 A334153

Keyword

nonn,base

Author

Michel Marcus, Apr 16 2020

Extensions

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

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

Status

approved