

A087242


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


3



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
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OFFSET

1,1


LINKS

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


FORMULA

a(n) = Min{x; 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: A322592 A329896 A303779 * A123556 A284017 A236454
Adjacent sequences: A087239 A087240 A087241 * A087243 A087244 A087245


KEYWORD

nonn


AUTHOR

Labos Elemer, Sep 04 2003


STATUS

approved



