A087242 Smallest prime number p such that n+p = q is also a prime, or 0 if no such prime number exists.

2, 3, 2, 3, 2, 5, 0, 3, 2, 3, 2, 5, 0, 3, 2, 3, 2, 5, 0, 3, 2, 7, 0, 5, 0, 3, 2, 3, 2, 7, 0, 5, 0, 3, 2, 5, 0, 3, 2, 3, 2, 5, 0, 3, 2, 7, 0, 5, 0, 3, 2, 7, 0, 5, 0, 3, 2, 3, 2, 7, 0, 5, 0, 3, 2, 5, 0, 3, 2, 3, 2, 7, 0, 5, 0, 3, 2, 5, 0, 3, 2, 7, 0, 5, 0, 3, 2, 13, 0, 7, 0, 5, 0, 3, 2, 5, 0, 3, 2, 3, 2, 5, 0, 3, 2

Offset: 1

Author

Labos Elemer, Sep 04 2003

Keywords

• nonn

Examples

			a(n)=0, i.e., no solution exists if n is a special prime, namely n is not a lesser twin prime; e.g., if n=7, then neither 7+2=9 nor 7+(odd prime) is a prime, thus no p prime exists such that 7+p is also a prime.
If n is a lesser twin prime then a(n)=2 is a solution because n+a(n) = n+2 = greater twin prime satisfying the condition.
		

Crossrefs

Cf. A087243, A174960.

Programs

PARI

a(n) = {if (n % 2, if (isprime(n+2), p = 2, p = 0);, p = 2; while (!isprime(n+p), p = nextprime(p+1));); p;} \\ Michel Marcus, Dec 26 2013

Formula

a(n) = Min{x prime; n+x is prime}.