1,1

For n>1, sequence gives primes ending in 3 or 7. - Lekraj Beedassy (blekraj(AT)yahoo.com), Oct 27 2003

Inert rational primes in Q(sqrt 5), or, 5 is not a square mod p.

Primes for which the period of the Fibonacci sequence mod p divides 2p+2.

Let F(n) be the n-th Fibonacci number for n=1,2,3... (A000045). F(n) mod p (a prime) generates a periodic sequence. This sequence may be generated as follows: F(p-1)* F(p) mod p = p-1. E.g. p=7: F(6)=8 * F(7)=13) then 8 * 13 mod 7 = 6 (p-1=6). - Louis Mello (Mellols(AT)aol.com), Feb 09 2001

These are also the primes p that divide Fibonacci(p+1) - Jud McCranie (j.mccranie(AT)comcast.net).

Also primes p such that p divides F(2p+1)-1; such that p divides F(2p+3)-1; such that p divides F(3p+1)-1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 05 2003

Primes p such that the polynomial x^2-x-1 mod p has no zeros; i.e. x^2-x-1 is irreducible over the integers mod p. - T. D. Noe (noe(AT)sspectra.com), May 02 2005

Hardy and Wright, An Introduction to the Theory of Numbers, Chap. X, p. 150, Oxford University Press, Fifth edition

H. Hasse, Number Theory, Springer-Verlag, NY, 1980, p. 498.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. N. Vorob'ev, Fibonacci Numbers, Pergamon Press, 1961.

T. D. Noe, Table of n, a(n) for n=1..1000

lst={}; Do[p=Prime[n]; If[Mod[p, 5]==2||Mod[p, 5]==3, AppendTo[lst, p]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 26 2009]

Sequence in context: A045329 A106306 A069104 this_sequence A032449 A129941 A159079

Adjacent sequences: A003628 A003629 A003630 this_sequence A003632 A003633 A003634

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein