A157188 Number of ways to write prime(n) as p*q-(p+q) with primes p<=q.

0, 2, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 3, 0, 0, 4, 0, 1, 1, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 1, 1, 0, 0, 1, 2, 0, 3, 0, 3, 0, 1, 1, 1, 1, 1, 0, 0, 3, 0, 2, 0, 2, 1, 1, 0, 1, 0, 0, 0, 4, 0, 0, 1, 0, 2, 0, 0, 4, 0, 0, 1, 2, 0, 0, 0, 0, 4, 0, 4, 0, 0, 1, 0, 0, 1, 1, 1, 3, 0, 1, 1, 3, 0, 1, 1, 0, 0, 0, 1, 1, 0

Offset: 1

Author

M. F. Hasler, Mar 11 2009

Keywords

• nonn

Comments

Records in this sequence are given in A157189, the corresponding primes in A157190.

Examples

			a(1)=0 since prime(1) = 2 cannot be written as pq-(p+q) for primes p,q.
a(2)=2 since prime(2) = 3 = 2*5-(2+5) = 3*3-(3+3) are the two possibilities.
		

Links

• C. Rivera (Ed.), Puzzle 482: Two Bergot questions, March 2009.

Crossrefs

Cf. A157187-A157190

Programs

PARI

A157188(n)={ local(c=0,L=sqrtint(n=prime(n)+1)); fordiv( n,d, d>L&break; isprime(d+1) || next; isprime(n/d+1) & c++);c}