A225581 a(n) is the minimal odd prime q such that prime(n)*q + prime(n) + q is prime.

3, 5, 3, 3, 3, 5, 3, 3, 7, 5, 3, 3, 3, 5, 3, 7, 3, 11, 3, 5, 5, 5, 5, 3, 5, 11, 17, 3, 3, 5, 47, 11, 5, 5, 3, 3, 3, 5, 13, 11, 3, 3, 5, 5, 5, 11, 11, 11, 3, 3, 7, 5, 3, 5, 3, 5, 5, 3, 5, 13, 11, 7, 3, 5, 11, 5, 3, 5, 5, 3, 19, 3, 3, 5, 29, 17, 3, 23, 3, 5, 7, 5, 5, 71, 3, 5, 5, 3, 3, 47, 3, 5, 3, 11, 3, 5, 3, 3, 11, 5, 23

Offset: 1

Author

John-Å. W. Olsen, May 11 2013

Keywords

• nonn
• easy

Examples

			n = 1;  p = 2;  q = 3;
n = 2;  p = 3;  q = 5;
n = 3;  p = 5;  q = 3;
n = 4;  p = 7;  q = 3;
		

Links

• John-Å. W. Olsen, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040.

Programs

Mathematica

a[n_] := Block[{q = 3, p = Prime@n},While[! PrimeQ[p*q + p + q], q = NextPrime@q]; q]; Array[a, 101] (* Giovanni Resta, May 11 2013 *)

PARI

a(n) = my(q=3, p=prime(n)); while(!isprime(p*q+p+q), q = nextprime(q+1)); q; \\ Michel Marcus, Sep 06 2021

Python

from sympy import isprime, nextprime, prime
def a(n):
    q, p = 3, prime(n)
    while not isprime(p*q + p + q): q = nextprime(q)
    return q
print([a(n) for n in range(1, 102)]) # Michael S. Branicky, Sep 06 2021