A098428 Number of sexy prime pairs (p, p+6) with p <= n.

0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15

Offset

1,7

Comments

Since there are 2 congruence classes of sexy prime pairs, (-1, -1) (mod 6) and (+1, +1) (mod 6), the number of sexy prime pairs up to n is the sum of the number of sexy prime pairs for each class, expected to be asymptotically the same for both (with the expected Chebyshev bias against the quadratic residue class (+1, +1) (mod 6), which doesn't affect the asymptotic distribution among the 2 classes). - Daniel Forgues, Aug 05 2009

Links

Daniel Forgues, Table of n, a(n) for n=1..99994

Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021]

Formula

a(n) = # { p in A023201 | p <= n } = number of elements in intersection of A023201 and [1,n]. - M. F. Hasler, Jan 02 2020

Example

The first sexy prime pairs are: (5,11), (7,13), (11,17), (13,19), ...
therefore the sequence starts: 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, ...

Mathematica

Accumulate[Table[If[PrimeQ[n]&&PrimeQ[n+6], 1, 0], {n, 100}]] (* Harvey P. Dale, Feb 08 2015 *)

Prog

(PARI) apply( {A098428(n, o=2, q=o, c)=forprime(p=1+q, n+6, (o+6==p)+((o=q)+6==q=p) && c++); c}, [1..99]) \\ M. F. Hasler, Jan 02 2020
[#[p:p in PrimesInInterval(1, n)| IsPrime(p+6)]:n in [1..100]]; // Marius A. Burtea, Jan 03 2020

Crossrefs

Cf. A023201, A046117, A098424, A071538, A098429.

Sequence in context: A209082 A257684 A098424 * A023193 A096605 A189671

Adjacent sequences: A098425 A098426 A098427 * A098429 A098430 A098431

Keyword

nonn

Author

Reinhard Zumkeller, Sep 07 2004

Extensions

Edited by Daniel Forgues, Aug 01 2009, M. F. Hasler, Jan 02 2020

Status

approved