login
Primes p such that Fibonacci(p)-1 is divisible by p.
15

%I #28 Sep 24 2022 14:01:47

%S 2,11,19,29,31,41,59,61,71,79,89,101,109,131,139,149,151,179,181,191,

%T 199,211,229,239,241,251,269,271,281,311,331,349,359,379,389,401,409,

%U 419,421,431,439,449,461,479,491,499,509,521,541,569,571,599,601,619

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

%H Harry J. Smith, <a href="/A064739/b064739.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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 *)

%t Select[Prime[Range[150]],Divisible[Fibonacci[#]-1,#]&] (* _Harvey P. Dale_, Sep 24 2022 *)

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

%o (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

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

%K nonn

%O 1,1

%A _Shane Findley_ and _N. J. A. Sloane_, Oct 17 2001

%E More terms from _Klaus Brockhaus_, Oct 18 2001