%I #20 May 08 2018 02:38:25

%S 93,117,119,121,123,143,145,185,187,203,205,207,215,217,219,245,247,

%T 287,289,297,299,301,303,321,323,325,327,341,343,363,393,405,413,415,

%U 425,427,453,471,473,475,483,495,513,515,517,527,529,531,533,535,537,551

%N Odd composite numbers n such that n-2 and n+2 are also composite.

%C No term is the difference of two primes. - _Juri-Stepan Gerasimov_, Oct 10 2009

%C Goldbach's conjecture states that all even numbers > 2 can be expressed as the sum of two primes. If true, then this sequence contains all composites which cannot be expressed as the sum or difference of two primes. - _Bob Selcoe_, Mar 10 2015

%H Michael De Vlieger, <a href="/A099019/b099019.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>

%e 93 is the first term because 91=7*13, 93=3*31 and 95=5*19 are all composite and there is no smaller odd composite with both odd neighbors composite.

%t Select[Range@1200, OddQ@# && AllTrue[{# - 2, #, # + 2}, CompositeQ] &] (* _Michael De Vlieger_, Mar 10 2015, Version 10 *)

%o (PARI) forstep(n=9,1000,2,if(!isprime(n)&&!isprime(n-2)&&!isprime(n+2),print1(n,",")))

%Y Subsequence of A007921.

%K nonn

%O 1,1

%A _Rick L. Shepherd_, Nov 13 2004