A064739 Primes p such that Fibonacci(p)-1 is divisible by p.

2, 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 349, 359, 379, 389, 401, 409, 419, 421, 431, 439, 449, 461, 479, 491, 499, 509, 521, 541, 569, 571, 599, 601, 619

Offset: 1

Author

Shane Findley and N. J. A. Sloane, Oct 17 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

{2} union A045468. Complement is A003631 minus {2}.

Programs

Mathematica

lst={};Do[p=Prime[n];If[Mod[(Fibonacci[p]-1),p]==0,AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Select[Prime[Range[150]],Divisible[Fibonacci[#]-1,#]&] (* Harvey P. Dale, Sep 24 2022 *)

PARI

forprime(p=2,700, if((fibonacci(p)-1)%p==0,print1(p,", ")))

PARI

{ n=0; for (m=1, 10^9, p=prime(m); if ((fibonacci(p) - 1)%p==0, write("b064739.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 24 2009

Formula

Presumably this consists of 2 together with the primes congruent to +-1 mod 5.

Extensions

More terms from Klaus Brockhaus, Oct 18 2001