OFFSET
1,1
COMMENTS
Alternately, for these primes p, the polynomial (x^p+1)/(x+1) is reducible over GF(2).
The prime p belongs to this sequence if and only if A002326((p-1)/2) != (p-1). If A002326((p-1)/2) = (p-1), then the prime p belongs to the sequence A001122. - V. Raman, Dec 01 2012
The only primitive root modulo 2 is 1. See A060749. Hence 2 should be added to this sequence in order to obtain the complement of A001122. - Wolfdieter Lang, May 19 2014
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Anand Bhardwaj, Luisa Degen, Radostin Petkov, and Sidney Stanbury, A Study of Cunningham Bounds through Rogue Primes, arXiv:2311.13375 [math.NT], 2023.
MAPLE
select(t -> isprime(t) and numtheory[order](2, t) <> t-1, [seq](2*i+1, i=1..1000)); # Robert Israel, May 20 2014
MATHEMATICA
Select[Prime[Range[2, 100]], PrimitiveRoot[#] =!= 2 &] (* T. D. Noe, Sep 19 2012 *)
PROG
(PARI) forprime(p=3, 1000, if(znorder(Mod(2, p))!=p-1, print(p)))
(PARI) forprime(p=3, 1000, if(factormod((x^p+1)/(x+1), 2, 1)[1, 1]!=(p-1), print(p)))
CROSSREFS
KEYWORD
nonn
AUTHOR
V. Raman, Sep 17 2012
EXTENSIONS
Name corrected by Wolfdieter Lang, May 19 2014
STATUS
approved