A047652 Primes for which golden mean is a cubic residue.

139, 151, 199, 331, 541, 619, 661, 709, 811, 829, 919, 1069, 1231, 1279, 1291, 1381, 1471, 1579, 1699, 1999, 2161, 2221, 2239, 2251, 2281, 2371, 2389, 2521, 2659, 2689, 2749, 3001, 3121, 3271, 3331, 3391, 3499, 3529, 3571, 3631, 3919, 4021, 4051, 4159

Offset

1,1

Comments

Primes of the form x^2 + xy + 34y^2, whose discriminant is -135. - T. D. Noe, May 17 2005

Primes of the form x^2 + 135*y^2. - Arkadiusz Wesolowski, May 31 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

E. Lehmer, On the quadratic character of the Fibonacci root, Fib. Quart., 4 (1966), 135-138.

E. Lehmer, On the quadratic character of the Fibonacci root (annotated scanned copy)

Formula

Primes p that divide Fibonacci((p-1)/3). - Alexander Adamchuk, Sep 16 2006

Mathematica

Select[Prime[Range[1000]], IntegerQ[Fibonacci[(#1-1)/3]/#1]&] (* Alexander Adamchuk, Sep 16 2006 *)

Crossrefs

Cf. A047650.

Sequence in context: A333135 A361342 A270310 * A308788 A308796 A334564

Adjacent sequences: A047649 A047650 A047651 * A047653 A047654 A047655

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Jan 25 2000

Status

approved