A066651 Primes of the form 2*s + 1, where s is a squarefree number (A005117).

3, 5, 7, 11, 13, 23, 29, 31, 43, 47, 53, 59, 61, 67, 71, 79, 83, 103, 107, 131, 139, 149, 157, 167, 173, 179, 191, 211, 223, 227, 229, 239, 263, 269, 277, 283, 293, 311, 317, 331, 347, 349, 359, 367, 373, 383, 389, 419, 421, 431

Offset

1,1

Comments

For these odd primes delta(p) = A055034(n) = (p-1)/2 is squarefree, and therefore the (Abelian) multiplicative group Modd p (see a comment on A203571 for Modd n, not to be confused with mod n) is guaranteed to be cyclic. This is because the number of Abelian groups of order n (A000688) is 1 precisely for the squarefree numbers A005117. See also A210845. One can in fact prove that the multiplicative group Modd p is cyclic for all primes (the case p=2 is trivial). - Wolfdieter Lang, Sep 24 2012

Links

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

Example

a(13) = A000040(18) = 61 = 2*30+1 = 2*A005117(19)+1.

Mathematica

Select[2 * Select[Range[200], SquareFreeQ] + 1, PrimeQ] (* Amiram Eldar, Feb 22 2021 *)

Prog

(PARI) isok(p) = isprime(p) && (p>2) && issquarefree((p-1)/2); \\ Michel Marcus, Feb 22 2021

Crossrefs

Cf. A005385, A066652, A066653.

Sequence in context: A174350 A240476 A040140 * A182583 A181741 A350401

Adjacent sequences: A066648 A066649 A066650 * A066652 A066653 A066654

Keyword

nonn

Author

Reinhard Zumkeller, Jan 10 2002

Status

approved