login
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.
1
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
1,1
LINKS
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
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 *)
PROG
(Magma) [(p+1)^2 div 3: p in PrimesInInterval(5, 1100) |IsPrime(p+2)]; // Marius A. Burtea, Jan 02 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanin (Mirza Sabbir Hossain Beg) (mirzasabbirhossainbeg(AT)yahoo.com), Sep 13 2009
EXTENSIONS
More terms from Robert G. Wilson v, Sep 13 2009
Edited by N. J. A. Sloane, Sep 15 2009
STATUS
approved