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

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

Offset: 1

Author

Roger L. Bagula, Apr 29 2006

Keywords

• nonn

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

• 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

Crossrefs

Cf. A108946.

Programs

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

Extensions

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

Edited by Joerg Arndt, Dec 30 2023