cp's OEIS Frontend

A243956 Positive numbers n without a decomposition into a sum n = i+j such that 6i-1, 6i+1, 6j-1, 6j+1 are twin primes.

%I A243956 #25 Jun 24 2014 13:18:18
%S A243956 1,16,67,86,131,151,186,191,211,226,541,701
%N A243956 Positive numbers n without a decomposition into a sum n = i+j such that 6i-1, 6i+1, 6j-1, 6j+1 are twin primes.
%C A243956 Conjecture: any integer n > 701 has a decomposition into a sum n = i+j such that 6i-1, 6i+1, 6j-1, 6j+1 are twin primes.
%p A243956 b:= n-> isprime(6*n-1) and isprime(6*n+1):
%p A243956 a:= proc(n) option remember; local i, k, ok;
%p A243956       for k from 1 +`if`(n=1, 0, a(n-1)) do ok:= true;
%p A243956         for i to iquo(k, 2) while ok
%p A243956           do ok:= not(b(i) and b(k-i)) od;
%p A243956         if ok then return k fi
%p A243956       od
%p A243956     end:
%p A243956 seq(a(n), n=1..12);  # _Alois P. Heinz_, Jun 20 2014
%o A243956 (PARI) l=List();a=select(p->isprime(p-2)&&p>5, primes(2000))\6;
%o A243956 for(i=1,#a-1,listput(l,2*a[i]);for(j=i+1,#a,listput(l,(a[i]+a[j]))));
%o A243956 print(setminus(Set(vector(l[#l]/4, i, i)), Set(l)))
%Y A243956 Cf. A002822, A187759.
%K A243956 nonn
%O A243956 1,2
%A A243956 _Lear Young_, Jun 15 2014