This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A254041 #18 Feb 16 2025 08:33:24
%S A254041 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 A254041 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 A254041 5,6,5,6,8,4,5,9,2,5,8,3,5,8,4,4,9,6,4,9
%N A254041 Number of decompositions of 2n into an unordered sum of two sexy primes.
%C A254041 "Sexy primes" are listed in A136207.
%C A254041 It is conjectured that a(n) > 0 for n > 4.
%H A254041 Lei Zhou, <a href="/A254041/b254041.txt">Table of n, a(n) for n = 1..10000</a>
%H A254041 Eric Weisstein's World of Math, <a href="https://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 A254041 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sexy_prime">Sexy Primes</a>
%H A254041 Lei Zhou, <a href="/A254041/a254041.jpg">Plot of a(n)</a> up to n=1000000.
%e A254041 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 A254041 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 A254041 Cf. A136207, A023201, A240712, A002375.
%K A254041 nonn,easy
%O A254041 1,9
%A A254041 _Lei Zhou_, Jan 23 2015