A165280 If p and q are twin primes then pq + 1 is always divisible by 3, except for (p,q)=(3,5). Sequence gives values of (pq + 1)/3.

12, 48, 108, 300, 588, 1200, 1728, 3468, 3888, 6348, 7500, 10800, 12288, 13068, 17328, 19200, 24300, 26508, 32448, 40368, 58800, 62208, 71148, 90828, 108300, 120000, 127308, 137388, 145200, 218700, 225228, 228528, 245388, 259308, 346800

Offset: 1

Author

Tanin (Mirza Sabbir Hossain Beg) (mirzasabbirhossainbeg(AT)yahoo.com), Sep 13 2009

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001097, A001359, A006512, A037074, A075369.

Programs

Magma

[(p+1)^2 div 3: p in PrimesInInterval(5,1100) |IsPrime(p+2)]; // Marius A. Burtea, Jan 02 2020

Mathematica

p = Rest@ Select[ Prime@ Range@ 175, PrimeQ[ # + 2] & ]; (p (p + 2) + 1)/3 (* Robert G. Wilson v, Sep 13 2009 *)
(Times@@#+1)/3&/@Select[Partition[Prime[Range[3,200]],2,1],#[[2]]-#[[1]] == 2&] (* Harvey P. Dale, Aug 28 2022 *)

Formula

a(n) = (A001359(n+1)*A006512(n+1)+1)/3 = (A037074(n+1)+1)/3 = A075369(n+1)/3. - Robert G. Wilson v, Sep 13 2009

Extensions

More terms from Robert G. Wilson v, Sep 13 2009

Edited by N. J. A. Sloane, Sep 15 2009