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.

1, 16, 67, 86, 131, 151, 186, 191, 211, 226, 541, 701

Offset: 1

Author

Lear Young, Jun 15 2014

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A002822, A187759.

Programs

Maple

b:= n-> isprime(6*n-1) and isprime(6*n+1):
a:= proc(n) option remember; local i, k, ok;
      for k from 1 +`if`(n=1, 0, a(n-1)) do ok:= true;
        for i to iquo(k, 2) while ok
          do ok:= not(b(i) and b(k-i)) od;
        if ok then return k fi
      od
    end:
seq(a(n), n=1..12);  # Alois P. Heinz, Jun 20 2014

PARI

l=List();a=select(p->isprime(p-2)&&p>5, primes(2000))\6;
for(i=1,#a-1,listput(l,2*a[i]);for(j=i+1,#a,listput(l,(a[i]+a[j]))));
print(setminus(Set(vector(l[#l]/4, i, i)), Set(l)))