A117808 Primes of the form ((2 + sqrt(3))^(2*n+1) + (2 - sqrt(3))^(2*n+1))/4.

3, 13, 181, 2521, 489061, 6811741, 1321442641, 18405321661, 381765135195632792959100810331957408101589361

Offset

1,1

Comments

Primes in A001570. - Joerg Arndt, Dec 30 2023

Primes among absolute values of A108946.

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

Links

Table of n, a(n) for n=1..9.

J. B. Cosgrave and K. Dilcher, The multiplicative orders of certain Gauss factorials, Intl. J. Number Theory 7 (1) (2011) 145-171.

John B. Cosgrave and Karl Dilcher, The multiplicative orders of certain Gauss factorials II, Funct. Approx. Comment. Math. Volume 54, Number 1 (2016), 73-93.

Christopher Stokes, On Gauss factorials and their application to Iwasawa theory for imaginary quadratic fields, arXiv:2207.07804 [math.NT], 2022.

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Prog

(PARI) b(n)=my(w=quadgen(12)); ((w+2)^n+(2-w)^n)\4
for(n=2, 800, if(isprime(p=b(n)), print1(p", "))) \\ Charles R Greathouse IV, Aug 22 2022

Crossrefs

Cf. A108946.

Sequence in context: A323134 A368499 A081299 * A002065 A302143 A087601

Adjacent sequences: A117805 A117806 A117807 * A117809 A117810 A117811

Keyword

nonn

Author

Roger L. Bagula, Apr 29 2006

Extensions

Definition and terms corrected by N. J. A. Sloane, May 21 2010

Edited by Joerg Arndt, Dec 30 2023

Status

approved