A241536 Smallest k>=1 such that prime(n)+k and prime(n)-k are both semiprimes, or a(n)=0 if there is no such k.

0, 0, 1, 3, 0, 9, 8, 15, 2, 4, 27, 2, 8, 8, 8, 2, 10, 4, 2, 6, 4, 14, 28, 2, 32, 10, 8, 12, 14, 2, 6, 2, 4, 6, 6, 8, 2, 20, 34, 4, 24, 4, 14, 8, 12, 14, 2, 14, 8, 8, 14, 20, 6, 2, 8, 4, 20, 18, 10, 14, 16, 2, 2, 8, 8, 12, 4, 2, 8, 22, 12, 18, 26, 8, 2, 12, 18

Offset: 1

Author

Vladimir Shevelev, Apr 25 2014

Keywords

• nonn

Comments

If a(n)=2, then prime(n)+2 and prime(n)-2 are both semiprimes; that is, prime(n) belongs to A063643. - Michel Marcus, Mar 26 2015

Crossrefs

Cf. A001358, A241531, A241533, A241535.

Programs

Mathematica

sks[n_]:=Module[{k=1,p=Prime[n]},While[PrimeOmega[p+k]!=2||PrimeOmega[p-k]!=2||p-k<4,If[p-k<3,Break[]];k++];If[p-k<4,0,k]]; Array[sks,80] (* Harvey P. Dale, Dec 09 2016 *)

PARI

a(n) = {p = prime(n); for (k=1, p-1, if ((bigomega(p-k)==2) && (bigomega(p+k) == 2), return (k));); return (0);} \\ Michel Marcus, Apr 25 2014

Extensions

More terms from Michel Marcus, Apr 25 2014

Name edited by Michel Marcus, Mar 26 2015