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A163780 Terms in A054639 equal to 3 mod 4.

%I A163780 #22 Mar 23 2018 11:24:41
%S A163780 3,11,23,35,39,51,83,95,99,119,131,135,155,179,183,191,231,239,243,
%T A163780 251,299,303,323,359,371,375,411,419,431,443,483,491,495,515,519,531,
%U A163780 543,575,611,615,639,651,659,683,719,723,743,755,771,779,783,791,803,831,879
%N A163780 Terms in A054639 equal to 3 mod 4.
%C A163780 Previous name was: a(n) is the n-th A^-_1-prime (Archimedes^-_1 prime).
%C A163780 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.
%H A163780 P. R. J. Asveld <a href="/A163780/b163780.txt">Table of n, a(n) for n=1..3378</a>.
%H A163780 P. R. J. Asveld, <a href="http://dx.doi.org/10.1016/j.dam.2011.07.019">Permuting operations on strings and their relation to prime numbers</a>, Discrete Applied Mathematics 159 (2011) 1915-1932.
%H A163780 P. R. J. Asveld, <a href="http://eprints.eemcs.utwente.nl/20685/">Permuting operations on strings and the distribution of their prime numbers</a> (2011), TR-CTIT-11-24, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
%H A163780 P. R. J. Asveld, <a href="http://eprints.eemcs.utwente.nl/15678/">Some Families of Permutations and Their Primes </a> (2009), TR-CTIT-09-27, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
%H A163780 P. R. J. Asveld, <a href="http://doc.utwente.nl/67513/">Permuting Operations on Strings-Their Permutations and Their Primes</a>, Twente University of Technology, 2014.
%o A163780 (PARI)
%o A163780 ok(n) = n%4==3 && isprime(2*n+1) && znorder(Mod(2, 2*n+1)) == n;
%o A163780 select(ok, [1..1000]) \\ _Andrew Howroyd_, Nov 11 2017
%Y A163780 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).
%K A163780 nonn
%O A163780 1,1
%A A163780 _Peter R. J. Asveld_, Aug 12 2009
%E A163780 a(33)-a(55) from _Andrew Howroyd_, Nov 11 2017
%E A163780 New name from _Andrey Zabolotskiy_, Mar 23 2018