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

1,1

Comments

Suggested by a comment by Alex Ratushnyak in A175330.

Links

Table of n, a(n) for n=1..14.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Positions of ones in A175330.

Cf. A007053, A214415.

Sequence in context: A148455 A094590 A004529 * A238236 A294159 A000778

Adjacent sequences: A366547 A366548 A366549 * A366551 A366552 A366553

Keyword

nonn,base,hard,more

Author

Paolo Xausa, Oct 13 2023

Status

approved