OFFSET
1,1
COMMENTS
Previous name was: a(n) is the n-th A^-_1-prime (Archimedes^-_1 prime).
N is A^-_1-prime iff N=3 (mod 4), p=2N+1 is a prime number and -2 generates Z_p^* (the multiplicative group of Z_p) but +2 does not.
LINKS
P. R. J. Asveld Table of n, a(n) for n=1..3378.
P. R. J. Asveld, Permuting operations on strings and their relation to prime numbers, Discrete Applied Mathematics 159 (2011) 1915-1932.
P. R. J. Asveld, Permuting operations on strings and the distribution of their prime numbers (2011), TR-CTIT-11-24, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
P. R. J. Asveld, Some Families of Permutations and Their Primes (2009), TR-CTIT-09-27, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology, 2014.
PROG
(PARI)
ok(n) = n%4==3 && isprime(2*n+1) && znorder(Mod(2, 2*n+1)) == n;
select(ok, [1..1000]) \\ Andrew Howroyd, Nov 11 2017
CROSSREFS
The A^-_1-primes are the T- or Twist-primes congruent 3 (mod 4), these T-primes are equal to the Queneau-numbers (A054639). For the related A_0-, A_1- and A^+_1-primes, see A163777, A163778 and A163779. Considered as sets the union of A163779 and A163780 equals A163778, the union of A163780 and A163777 is equal to A163781 (dual J_2-primes).
KEYWORD
nonn
AUTHOR
Peter R. J. Asveld, Aug 12 2009
EXTENSIONS
a(33)-a(55) from Andrew Howroyd, Nov 11 2017
New name from Andrey Zabolotskiy, Mar 23 2018
STATUS
approved