

A163780


Terms in A054639 equal to 3 mod 4.


7



3, 11, 23, 35, 39, 51, 83, 95, 99, 119, 131, 135, 155, 179, 183, 191, 231, 239, 243, 251, 299, 303, 323, 359, 371, 375, 411, 419, 431, 443, 483, 491, 495, 515, 519, 531, 543, 575, 611, 615, 639, 651, 659, 683, 719, 723, 743, 755, 771, 779, 783, 791, 803, 831, 879
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OFFSET

1,1


COMMENTS

Previous name was: a(n) is the nth A^_1prime (Archimedes^_1 prime).
N is A^_1prime 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) 19151932.
P. R. J. Asveld, Permuting operations on strings and the distribution of their prime numbers (2011), TRCTIT1124, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
P. R. J. Asveld, Some Families of Permutations and Their Primes (2009), TRCTIT0927, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
P. R. J. Asveld, Permuting Operations on StringsTheir 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^_1primes are the T or Twistprimes congruent 3 (mod 4), these Tprimes are equal to the Queneaunumbers (A054639). For the related A_0, A_1 and A^+_1primes, 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_2primes).
Sequence in context: A163769 A100860 A018630 * A094379 A072671 A320901
Adjacent sequences: A163777 A163778 A163779 * A163781 A163782 A163783


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



