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%I #32 Oct 30 2023 18:06:10
%S 1,2,7,8,12,14,15,29,34,44,51,62,68,76,79,91,99,100,107,125,142,147,
%T 156,162,163,173,190,202,212,231,245,252,253,264,295,306,317,330,331,
%U 355,366,376,377,386,397,442,448,453,462,469,481,491,498,502,516,547
%N Numbers k such that (6*k)^2 is the sum of a twin prime pair.
%H Amiram Eldar, <a href="/A037073/b037073.txt">Table of n, a(n) for n = 1..10000</a>
%H C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=TwinPrime">Twin primes</a>
%F a(n) = A173165(n)/3. - _M. F. Hasler_, Oct 30 2023
%e E.g. n=44 -> (6*44)^2 = 69696 = 34847 + 34849 (twin prime pair).
%p isa := n -> isprime(n) and isprime(n+2) and issqr(2*n+2):
%p select(isa, [$4..1000000]): map(n -> sqrt(2*n+2)/6, %); # _Peter Luschny_, Jan 05 2020
%t Select[Sqrt[Plus@@@Select[Partition[Prime[Range[4*10^5]],2,1],Differences[#]=={2} &]/36],IntegerQ] (* _Jayanta Basu_, May 26 2013 *)
%o (PARI) is(n)=isprime(18*n^2-1)&&isprime(18*n^2+1) \\ _M. F. Hasler_, Oct 30 2023
%Y Cf. A000290, A001359, A006512, A173165.
%Y A152786 = 6*A037073. - _Zak Seidov_, Aug 20 2010
%K nonn
%O 1,2
%A _G. L. Honaker, Jr._
%E More terms from _Jud McCranie_, Dec 30 2000
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