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

1,2

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.

Links

Table of n, a(n) for n=1..12.

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

Prog

(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)))

Crossrefs

Cf. A002822, A187759.

Sequence in context: A043933 A329530 A218646 * A216306 A321180 A100186

Adjacent sequences: A243953 A243954 A243955 * A243957 A243958 A243959

Keyword

nonn

Author

Lear Young, Jun 15 2014

Status

approved