A087242 - OEIS

%I #19 Aug 02 2021 04:45:58

%S 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,

%T 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,

%U 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

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

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

%e 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.

%e 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.

%o (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

%Y Cf. A087243, A174960.

%K nonn

%O 1,1

%A _Labos Elemer_, Sep 04 2003