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A167379 Let p and q be twin primes, excluding the pair (3,5). Then p+q is always divisible by 6 and we set a(n) = (p+q)/6.

%I A167379 #15 Sep 08 2022 08:45:48
%S A167379 2,4,6,10,14,20,24,34,36,46,50,60,64,66,76,80,90,94,104,116,140,144,
%T A167379 154,174,190,200,206,214,220,270,274,276,286,294,340,344,350,354,364,
%U A167379 384,410,426,430,434,440,476,484,494,496,536,540,556,566,574,596,624,626
%N A167379 Let p and q be twin primes, excluding the pair (3,5). Then p+q is always divisible by 6 and we set a(n) = (p+q)/6.
%C A167379 By definition, q = p+2. Hence (p+q)/6 = (p+p+2)/6 = (2p+2)/6 = (p+1)/3. Thus a(n) = (1+A001359(n+1))/3. - _Jonathan Vos Post_, Nov 03 2009
%H A167379 Vincenzo Librandi, <a href="/A167379/b167379.txt">Table of n, a(n) for n = 1..2000</a>
%F A167379 a(n) = 2*A002822(n). - _R. J. Mathar_, Nov 09 2009
%F A167379 a(n) = (1+A001359(n+1))/3. - _Jonathan Vos Post_, Nov 03 2009
%e A167379 First (lesser of twin prime pair) excluding (3,5) = 5; (5+1)/3 = 2, hence A167379(1) = 2. The 10th (lesser of twin prime pair) excluding (3,5) = 137; (137+1)/3 = 46, hence A167379(10)= 46. - _Jonathan Vos Post_, Nov 03 2009
%t A167379 Total[#]/6&/@Select[Partition[Prime[Range[3,500]],2,1],#[[2]]-#[[1]] == 2&] (* _Harvey P. Dale_, Jan 30 2013 *)
%t A167379 2 Select[Range[35000], PrimeQ[6 # - 1] && PrimeQ[6 # + 1] &] (* _Vincenzo Librandi_, Jun 13 2016 *)
%o A167379 (Magma) [2*n: n in [1..630] | IsPrime(6*n+1) and IsPrime(6*n-1)]; // _Vincenzo Librandi_, Jun 13 2016
%Y A167379 Cf. A002822. [_Zak Seidov_, Nov 02 2009]
%K A167379 nonn
%O A167379 1,1
%A A167379 Tanin (Mirza Sabbir Hossain Beg) (mirzasabbirhossainbeg(AT)yahoo.com), Nov 02 2009
%E A167379 Edited (but not checked) by _N. J. A. Sloane_, Nov 02 2009
%E A167379 Extended by _R. J. Mathar_, Nov 09 2009