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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.

%I A165280 #17 Sep 08 2022 08:45:47
%S A165280 12,48,108,300,588,1200,1728,3468,3888,6348,7500,10800,12288,13068,
%T A165280 17328,19200,24300,26508,32448,40368,58800,62208,71148,90828,108300,
%U A165280 120000,127308,137388,145200,218700,225228,228528,245388,259308,346800
%N 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.
%H A165280 Amiram Eldar, <a href="/A165280/b165280.txt">Table of n, a(n) for n = 1..10000</a>
%F A165280 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
%t A165280 p = Rest@ Select[ Prime@ Range@ 175, PrimeQ[ # + 2] & ]; (p (p + 2) + 1)/3 (* _Robert G. Wilson v_, Sep 13 2009 *)
%t A165280 (Times@@#+1)/3&/@Select[Partition[Prime[Range[3,200]],2,1],#[[2]]-#[[1]] == 2&] (* _Harvey P. Dale_, Aug 28 2022 *)
%o A165280 (Magma) [(p+1)^2 div 3: p in PrimesInInterval(5,1100) |IsPrime(p+2)]; // _Marius A. Burtea_, Jan 02 2020
%Y A165280 Cf. A001097, A001359, A006512, A037074, A075369.
%K A165280 nonn
%O A165280 1,1
%A A165280 Tanin (Mirza Sabbir Hossain Beg) (mirzasabbirhossainbeg(AT)yahoo.com), Sep 13 2009
%E A165280 More terms from _Robert G. Wilson v_, Sep 13 2009
%E A165280 Edited by _N. J. A. Sloane_, Sep 15 2009