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Squarefree numbers k such that the pair 2*k +- 1 is a twin prime pair.
4

%I #21 Jul 26 2022 16:04:08

%S 2,3,6,15,21,30,51,69,114,141,174,210,231,285,309,321,330,411,429,510,

%T 546,615,645,651,714,741,834,849,861,894,939,966,1041,1065,1119,1155,

%U 1191,1329,1365,1401,1626,1686,1695,1731,1770

%N Squarefree numbers k such that the pair 2*k +- 1 is a twin prime pair.

%H Amiram Eldar, <a href="/A066653/b066653.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 3*A355846(n-1), for n >= 2. - _Wesley Ivan Hurt_, Jul 24 2022

%e 2*a(6) +/- 1 = 2*30 +/- 1 = (59, 61) = (A000040(17), A000040(18)) = (A001359(7), A006512(7)) = (A066652(10), A066651(13)).

%t Select[Range[2000], SquareFreeQ[#] && And @@ PrimeQ[2# + {-1, 1}] &] (* _Amiram Eldar_, Dec 19 2019 *)

%o (Magma) [k:k in [1..2000]|IsSquarefree(k) and IsPrime(2*k-1) and IsPrime(2*k+1)]; // _Marius A. Burtea_, Dec 19 2019

%o (PARI) isok(k) = issquarefree(k) && isprime(2*k-1) && isprime(2*k+1); \\ _Michel Marcus_, Jul 25 2022

%Y Cf. A014574, A001359, A006512, A066651, A066652, A355846.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jan 10 2002