A163857 Number of sexy prime quadruples (p, p+6, p+12, p+18), with p <= n.

0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 1

Author

Daniel Forgues, Aug 05 2009

Keywords

• nonn

Comments

There are 2 sexy prime quadruples classes, (-1, -1, -1, -1) (mod 6) and (+1, +1, +1, +1) (mod 6). They should asymptotically have the same number of quadruples, if there is an infinity of such quadruples, although with a Chebyshev bias expected against the quadratic residue class quadruples (+1, +1, +1, +1) (mod 6), which doesn't affect the asymptotic result. This sequence counts both classes.

Also the sexy prime quadruples of class (-1, -1, -1, -1) (mod 6) are (11, 17, 23, 29) (mod 30) while the sexy prime quadruples of class (+1, +1, +1, +1) (mod 6) are (1, 7, 13, 19) (mod 30).

Except for (5, 11, 17, 23, 29), there is no sexy prime quintuples (p, p+6, p+12, p+18, p+24) since one of the members is then divisible by 5.

Links

• Daniel Forgues, Table of n, a(n) for n=1..99982
• Eric Weisstein's World of Mathematics, Prime Constellation

Crossrefs

A023271 First member of a sexy prime quadruple: value of p where (p, p+6, p+12, p+18) are all prime.

A046122 Second member of a sexy prime quadruple: value of p+6 where (p, p+6, p+12, p+18) are all prime.

A046123 Third member of a sexy prime quadruple: value of p+12 where (p, p+6, p+12, p+18) are all prime.

A046124 Last member of a sexy prime quadruple: value of p+18 where (p, p+6, p+12, p+18) are all prime.