A366550 Numbers k such that bitwise AND of prime(k) and prime(k+1) = 1.

2, 6, 18, 54, 564, 3512, 6542, 564163, 2063689, 54400028, 5586502348, 252252704148404, 971269945245201, 3745011184713964

Offset: 1

Author

Paolo Xausa, Oct 13 2023

Keywords

• nonn
• base
• hard
• more

Comments

Suggested by a comment by Alex Ratushnyak in A175330.

Examples

			18 is a term since prime(18) AND prime(19) = 1,
  prime(18) = 61 = binary 0111101
  prime(19) = 67 = binary 1000011
  bitwise AND    =        0000001
		

Crossrefs

Positions of ones in A175330.

Cf. A007053, A214415.

Programs

Mathematica

A366550list[upto_]:=PrimePi[Select[2^Range[upto],BitAnd[NextPrime[#],NextPrime[#,-1]]==1&]];
A366550list[37] (* Uses formula, considering values in A214415 up to 37 *)

PARI

isok(k) = bitand(prime(k), prime(k+1)) == 1; \\ Michel Marcus, Oct 14 2023

Formula

a(n) = A007053(A214415(n-1)).