A230010 a(n) = smallest prime p such that n*(p^2 + 1) + 1 is also prime or 0 if no such prime exists.

3, 2, 3, 3, 5, 2, 3, 2, 13, 3, 13, 2, 3, 2, 3, 0, 5, 3, 3, 2, 3, 0, 5, 3, 3, 2, 3, 3, 7, 2, 3, 7, 3, 0, 5, 2, 0, 2, 7, 3, 11, 2, 3, 13, 5, 3, 5, 2, 3, 2, 5, 3, 13, 2, 0, 2, 3, 0, 23, 3, 0, 2, 3, 3, 7, 2, 0, 11, 3, 3, 5, 5, 0, 7, 3, 3, 5, 5, 0, 2, 3, 3, 17, 2

Offset

1,1

Comments

If n*3^2+n+1 is not prime and (n-1) is divisible by 3 then a(n) = 0.

The first such case is n = 16 when 161 is not prime and (16-1) is 5*3, while a(1,4,7,10,13) = 3.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

a(4) = 3, since p = 3 is prime and 4*p^2 + 4 + 1 = 36 + 4 + 1 = 41 is also prime.

Prog

(PARI) a(n) = {if (! isprime(10*n+1) && !((n-1) % 3), return (0)); p = 2; while ( !isprime(n*p^2 + n + 1), p = nextprime(p+1)); p; } \\ Michel Marcus, Dec 20 2013

Crossrefs

Sequence in context: A242409 A317623 A286244 * A380344 A230847 A234300

Adjacent sequences: A230007 A230008 A230009 * A230011 A230012 A230013

Keyword

nonn

Author

Zak Seidov, Dec 20 2013

Status

approved