

A163857


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


1



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
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OFFSET

1,11


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.
Sequence in context: A242253 A071839 A235044 * A185715 A111893 A121902
Adjacent sequences: A163854 A163855 A163856 * A163858 A163859 A163860


KEYWORD

nonn


AUTHOR

Daniel Forgues, Aug 05 2009


STATUS

approved



