A294078 a(n) is the smallest even number k such that k*prime(n) - 1 or k*prime(n) + 1 is prime.

2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 6, 2, 6, 6, 4, 4, 4, 2, 2, 2, 2, 6, 6, 6, 6, 2, 4, 2, 4, 2, 8, 6, 2, 4, 10, 2, 2, 6, 2, 4, 4, 2, 2, 8, 4, 2, 2, 2, 6, 2, 6, 4, 6, 2, 4, 2, 6, 2, 2, 6, 6, 6, 2, 2, 6, 8, 10, 2, 2, 4, 2, 4, 6, 6, 8, 4

Offset: 1

Author

Dimitris Valianatos, Feb 07 2018

Keywords

• nonn

Comments

For n <= 10^9 the largest term is 186.

First occurrence of 2k, k=1,2,3,...: 1, 6, 15, 35, 39, 117, 1134, 199, 152, 362, ..., . - Robert G. Wilson v, Feb 08 2018

Examples

			For n = 6, prime(6) = 13. The smallest even number k such that k * 13 + 1 is a prime number is k = 4, because 4 * 13 + 1 = 53 (not k = 2). So 4 is the sixth term.
		

Crossrefs

Cf. A000040, A071407 (with "and" rather than "or").

Programs

Mathematica

f[n_] := Block[{k = 2, p = Prime@ n}, While[ !PrimeQ[k*p -1] && !PrimeQ[k*p +1], k += 2]; k]; Array[f, 100] (* Robert G. Wilson v, Feb 08 2018 *)

PARI

{
  forprime(p=2,100,
    k=2;
    while(!isprime(k*p-1)&&!isprime(k*p+1),k+=2);
    print1(k", ");
  )
}