login
A366550
Numbers k such that bitwise AND of prime(k) and prime(k+1) = 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.
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.
Sequence in context: A148455 A094590 A004529 * A238236 A294159 A000778
KEYWORD
nonn,base,hard,more
AUTHOR
Paolo Xausa, Oct 13 2023
STATUS
approved