OFFSET
1,9
COMMENTS
"Sexy primes" are listed in A136207.
It is conjectured that a(n) > 0 for n > 4.
LINKS
Lei Zhou, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Math, Sexy Primes. [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]
Wikipedia, Sexy Primes
Lei Zhou, Plot of a(n) up to n=1000000.
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lei Zhou, Jan 23 2015
STATUS
approved