A066653 Squarefree numbers k such that the pair 2*k +- 1 is a twin prime pair.

2, 3, 6, 15, 21, 30, 51, 69, 114, 141, 174, 210, 231, 285, 309, 321, 330, 411, 429, 510, 546, 615, 645, 651, 714, 741, 834, 849, 861, 894, 939, 966, 1041, 1065, 1119, 1155, 1191, 1329, 1365, 1401, 1626, 1686, 1695, 1731, 1770

Offset: 1

Author

Reinhard Zumkeller, Jan 10 2002

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Magma

[k:k in [1..2000]|IsSquarefree(k) and IsPrime(2*k-1) and IsPrime(2*k+1)]; // Marius A. Burtea, Dec 19 2019

Mathematica

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

PARI

isok(k) = issquarefree(k) && isprime(2*k-1) && isprime(2*k+1); \\ Michel Marcus, Jul 25 2022

Formula

a(n) = 3*A355846(n-1), for n >= 2. - Wesley Ivan Hurt, Jul 24 2022