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A066651
Primes of the form 2*s + 1, where s is a squarefree number (A005117).
4
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 10 2002
STATUS
approved