OFFSET
1,1
COMMENTS
Primes p such that the smallest positive k such that p divides 3^k - 2^k is p - 1.
All terms are congruent to 7, 11, 13, 17 modulo 24. For other primes p, 3/2 is a quadratic residue modulo p.
By Artin's conjecture, this sequence contains 37.395% of all primes, or 74.79% of all primes congruent to 7, 11, 13, 17 modulo 24.
LINKS
C. Hooley, On Artin's conjecture, J. reine angewandte Math., 225 (1967) 209-220.
Wikipedia, Artin's conjecture on primitive roots
Wikipedia, Primitive root modulo n
EXAMPLE
3/2 == 5 (mod 7), 5 is a primitive root modulo 7, so 7 is a term. Indeed, 7 does not divide 3^2 - 2^2 or 3^3 - 2^3, but it divides 3^6 - 2^6.
3/2 == 7 (mod 11), 7 is a primitive root modulo 11, so 11 is a term. Indeed, 11 does not divide 3^2 - 2^2 or 3^5 - 2^5, but it divides 3^10 - 2^10.
3/2 == 13 (mod 23), 13^11 == 1 (mod 23), so 23 is not a term. Indeed, 23 divides 3^11 - 2^11.
PROG
(PARI) forprime(p=5, 10^3, if(p-1==znorder(Mod(3/2, p)), print1(p, ", "))); \\ Joerg Arndt, Oct 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Oct 12 2018
STATUS
approved