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%I #29 Dec 30 2023 12:10:16
%S 3,13,181,2521,489061,6811741,1321442641,18405321661,
%T 381765135195632792959100810331957408101589361
%N Primes of the form ((2 + sqrt(3))^(2*n+1) + (2 - sqrt(3))^(2*n+1))/4.
%C Primes in A001570. - _Joerg Arndt_, Dec 30 2023
%C Primes among absolute values of A108946.
%C Also the Cosgrave-Dilcher primes that are a subset of the nontrivial cyclotomic lambda invariant for Q(sqrt{-3}) (or a subset of the 1-exceptional primes for M=3). - _Christopher M. Stokes_, Aug 04 2022
%H J. B. Cosgrave and K. Dilcher, <a href="https://doi.org/10.1142/S179304211100396X">The multiplicative orders of certain Gauss factorials</a>, Intl. J. Number Theory 7 (1) (2011) 145-171.
%H John B. Cosgrave and Karl Dilcher, <a href="https://doi.org/10.7169/facm/2016.54.1.7">The multiplicative orders of certain Gauss factorials II</a>, Funct. Approx. Comment. Math. Volume 54, Number 1 (2016), 73-93.
%H Christopher Stokes, <a href="https://arxiv.org/abs/2207.07804">On Gauss factorials and their application to Iwasawa theory for imaginary quadratic fields</a>, arXiv:2207.07804 [math.NT], 2022.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%o (PARI) b(n)=my(w=quadgen(12)); ((w+2)^n+(2-w)^n)\4
%o for(n=2,800, if(isprime(p=b(n)), print1(p", "))) \\ _Charles R Greathouse IV_, Aug 22 2022
%Y Cf. A108946.
%K nonn
%O 1,1
%A _Roger L. Bagula_, Apr 29 2006
%E Definition and terms corrected by _N. J. A. Sloane_, May 21 2010
%E Edited by _Joerg Arndt_, Dec 30 2023
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