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

1,1

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A087243, A174960.

Sequence in context: A329896 A366262 A303779 * A123556 A284017 A236454

Adjacent sequences: A087239 A087240 A087241 * A087243 A087244 A087245

Keyword

nonn

Author

Labos Elemer, Sep 04 2003

Status

approved