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

1,4

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

Links

Table of n, a(n) for n=1..77.

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 *)

Prog

(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

Crossrefs

Cf. A001358, A241531, A241533, A241535.

Sequence in context: A197689 A201942 A181831 * A080407 A197335 A248885

Adjacent sequences: A241533 A241534 A241535 * A241537 A241538 A241539

Keyword

nonn

Author

Vladimir Shevelev, Apr 25 2014

Extensions

More terms from Michel Marcus, Apr 25 2014

Name edited by Michel Marcus, Mar 26 2015

Status

approved