A243154 Smallest k>=0 such that prime(n)*prime(n+k)-2 is prime.

0, 0, 0, 0, 4, 0, 2, 0, 4, 0, 7, 0, 4, 0, 0, 4, 11, 0, 2, 0, 4, 7, 7, 0, 12, 4, 0, 0, 2, 9, 0, 0, 2, 0, 6, 2, 1, 4, 10, 0, 13, 4, 0, 4, 10, 4, 0, 0, 2, 8, 0, 0, 5, 6, 0, 30, 20, 16, 4, 11, 7, 0, 5, 13, 0, 11, 18, 0, 2, 18, 5, 0, 1, 4, 5, 10, 4, 7, 4, 5, 11

Offset: 1

Author

Vladimir Shevelev, May 31 2014

Keywords

• nonn

Comments

One of the possible illustrations of Chen's theorem: there are infinitely many primes p such that p+2 is semiprime.

For a dual sequence, see A243158.

Crossrefs

Cf. A243158.

Programs

Mathematica

skp[n_]:=Module[{k=0,p=Prime[n]},While[!PrimeQ[p Prime[n+k]-2],k++];k]; Array[skp,90] (* Harvey P. Dale, Aug 15 2021 *)

PARI

vector(1000, n, k=0; while(!isprime(prime(n)*prime(n+k)-2), k++); k) \\ Colin Barker, May 31 2014

Extensions

a(25) corrected and more terms from Colin Barker, May 31 2014