OFFSET
0,1
COMMENTS
Primes of the form x^2 + 20*y^2. - T. D. Noe, May 08 2005
Also primes p that divide the sum of cubes of the first (p-1)/2 Fibonacci numbers A005968((p-1)/2). - Alexander Adamchuk, Aug 07 2006
From A.H.M. Smeets, Nov 16 2023: (Start)
Mean gap size between two consecutive terms at p: ~ 8*log(p).
In x^2 + 20y^2: x == 1 (mod 2) and x !== 5 (mod 10). Otherwise not prime. (End)
LINKS
A.H.M. Smeets, Table of n, a(n) for n = 0..20000 (terms 0..1700 from Vincenzo Librandi)
Bob Bastasz, Lyndon words of a second-order recurrence, Fibonacci Quarterly (2020) Vol. 58, No. 5, 25-29.
E. Lehmer, On the quadratic character of the Fibonacci root, Fib. Quart., 4 (1966), 135-138.
E. Lehmer, Correction, Fib. Quart., 4 (1966), 135-138.
E. Lehmer, On the quadratic character of the Fibonacci root (annotated scanned copy)
FORMULA
MATHEMATICA
nn=20; pMax=3000; Union[Reap[Do[p=x^2 + nn*y^2; If[p<=pMax&&PrimeQ[p], Sow[p]], {x, Sqrt[pMax]}, {y, Sqrt[pMax/nn]}]][[2, 1]]] (* Vincenzo Librandi, Sep 05 2016 *)
PROG
(Magma) k:=20; [p: p in PrimesUpTo(3000) | NormEquation(k, p) eq true]; // Vincenzo Librandi, Sep 05 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Jan 25 2000
STATUS
approved