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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 (list; graph; refs; listen; history; text; internal format)
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).

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

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Last modified September 29 10:54 EDT 2020. Contains 337428 sequences. (Running on oeis4.)