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

%I A163857 #6 Feb 16 2025 08:33:11
%S A163857 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,
%T A163857 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,
%U A163857 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
%N A163857 Number of sexy prime quadruples (p, p+6, p+12, p+18), with p <= n.
%C A163857 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.
%C A163857 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).
%C A163857 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.
%H A163857 Daniel Forgues, <a href="/A163857/b163857.txt">Table of n, a(n) for n=1..99982</a>
%H A163857 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a>
%Y A163857 A023271 First member of a sexy prime quadruple: value of p where (p, p+6, p+12, p+18) are all prime.
%Y A163857 A046122 Second member of a sexy prime quadruple: value of p+6 where (p, p+6, p+12, p+18) are all prime.
%Y A163857 A046123 Third member of a sexy prime quadruple: value of p+12 where (p, p+6, p+12, p+18) are all prime.
%Y A163857 A046124 Last member of a sexy prime quadruple: value of p+18 where (p, p+6, p+12, p+18) are all prime.
%K A163857 nonn
%O A163857 1,11
%A A163857 _Daniel Forgues_, Aug 05 2009