A230010 - OEIS

%I #18 Dec 23 2013 12:34:41

%S 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,

%T 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,

%U 2,0,11,3,3,5,5,0,7,3,3,5,5,0,2,3,3,17,2

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

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

%C 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.

%H Zak Seidov, <a href="/A230010/b230010.txt">Table of n, a(n) for n = 1..1000</a>

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

%o (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

%K nonn

%O 1,1

%A _Zak Seidov_, Dec 20 2013