%I #17 Mar 07 2021 00:56:09
%S 0,0,0,0,1,1,1,1,2,1,2,3,2,2,3,1,3,4,2,2,4,2,3,5,3,3,5,2,4,6,2,4,6,2,
%T 4,6,4,3,6,4,3,7,4,3,8,3,4,7,3,4,7,4,5,7,5,5,9,5,5,12,4,4,10,3,5,7,4,
%U 5,6,5,6,8,4,5,9,2,5,8,3,5,8,4,4,9,6,4,9
%N Number of decompositions of 2n into an unordered sum of two sexy primes.
%C "Sexy primes" are listed in A136207.
%C It is conjectured that a(n) > 0 for n > 4.
%H Lei Zhou, <a href="/A254041/b254041.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Math, <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]
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sexy_prime">Sexy Primes</a>
%H Lei Zhou, <a href="/A254041/a254041.jpg">Plot of a(n)</a> up to n=1000000.
%e When n = 79, 2n = 158 = 7 + 151 = 19 + 139 = 31 + 127 = 61 + 97 = 79 + 79 has five "two prime decompositions". Among the involved prime numbers 7, 19, 31, 61, 79, 97, 127, 139, 151, prime 127 and 139 are not sexy primes. So only three decompositions, 158 = 7 + 151 = 61 + 97 = 79 + 79 satisfy the definition of this sequence. Thus a(79) = 3.
%t Table[e = 2 n; ct = 0; p = 2; While[p = NextPrime[p]; p <= n, q = e - p; If[PrimeQ[q], If[(((p > 6) && PrimeQ[p - 6]) || PrimeQ[p + 6]) && (((q > 6) && PrimeQ[q - 6]) || PrimeQ[q + 6]), ct++]]]; ct, {n, 87}]
%Y Cf. A136207, A023201, A240712, A002375.
%K nonn,easy
%O 1,9
%A _Lei Zhou_, Jan 23 2015
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