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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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Daniel Forgues, Aug 05 2009
STATUS
approved

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Last modified June 22 14:17 EDT 2024. Contains 373587 sequences. (Running on oeis4.)