|
%I #16 Mar 07 2021 00:56:09
%S 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,
%T 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,
%U 12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,15,15,15
%N Number of sexy prime pairs (p, p+6) with p <= n.
%C 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
%H Daniel Forgues, <a href="/A098428/b098428.txt">Table of n, a(n) for n=1..99994</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SexyPrimes.html">Sexy Primes</a>. [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]
%F a(n) = # { p in A023201 | p <= n } = number of elements in intersection of A023201 and [1,n]. - _M. F. Hasler_, Jan 02 2020
%e The first sexy prime pairs are: (5,11), (7,13), (11,17), (13,19), ...
%e therefore the sequence starts: 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, ...
%t Accumulate[Table[If[PrimeQ[n]&&PrimeQ[n+6],1,0],{n,100}]] (* _Harvey P. Dale_, Feb 08 2015 *)
%o (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
%o [#[p:p in PrimesInInterval(1,n)| IsPrime(p+6)]:n in [1..100]]; // _Marius A. Burtea_, Jan 03 2020
%Y Cf. A023201, A046117, A098424, A071538, A098429.
%K nonn
%O 1,7
%A _Reinhard Zumkeller_, Sep 07 2004
%E Edited by _Daniel Forgues_, Aug 01 2009, _M. F. Hasler_, Jan 02 2020
|
