A244570 Smallest prime p >= prime(n) such that p*prime(n)+2 is prime.

3, 7, 11, 19, 17, 37, 23, 37, 43, 47, 47, 61, 53, 73, 109, 79, 89, 71, 109, 227, 113, 97, 139, 137, 127, 149, 127, 131, 283, 137, 139, 181, 173, 151, 167, 191, 173, 193, 193, 181, 239, 199, 233, 223, 239, 251, 239, 241, 233, 313, 241, 251, 271, 277, 373, 271

Offset: 2

Author

Vladimir Shevelev, Jun 30 2014

Keywords

• nonn

Comments

See comment in A244572.

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 2..10000
• V. Shevelev, Theorems on twin primes-dual case, arXiv:0912.4006 [math.GM], 2009-2014. Sections 10,14.

Crossrefs

Cf. A242719, A242720.

Programs

Mathematica

a[n_] := For[p = Prime[n], True, p = NextPrime[p], If[PrimeQ[p Prime[n] + 2], Return[p]]];
Table[a[n], {n, 2, 60}] (* Jean-François Alcover, Nov 18 2018 *)
sp[n_]:=Module[{p=n},While[CompositeQ[p*n+2],p=NextPrime[p]];p]; Table[ sp[k],{k,Prime[Range[2,60]]}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 19 2020 *)

PARI

s=[]; for(n=2, 100, p=q=prime(n); while(!isprime(p*q+2), p=nextprime(p+1)); s=concat(s, p)); s \\ Colin Barker, Jun 30 2014

Extensions

More terms from Peter J. C. Moses, Jun 30 2014