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

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(Magma) [k:k in [1..2000]|IsSquarefree(k) and IsPrime(2*k-1) and IsPrime(2*k+1)]; // Marius A. Burtea, Dec 19 2019
(PARI) isok(k) = issquarefree(k) && isprime(2*k-1) && isprime(2*k+1); \\ Michel Marcus, Jul 25 2022

Crossrefs

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

Sequence in context: A090983 A198684 A293534 * A081945 A329745 A255353

Adjacent sequences: A066650 A066651 A066652 * A066654 A066655 A066656

Keyword

nonn

Author

Reinhard Zumkeller, Jan 10 2002

Status

approved