A133247 Prime numbers p with property that no odd Fibonacci number is divisible by p.

2, 17, 19, 23, 31, 53, 61, 79, 83, 107, 109, 137, 167, 173, 181, 197, 211, 227, 229, 241, 257, 271, 293, 317, 349, 379, 383, 409, 421, 439, 443, 467, 499, 503, 541, 571, 587, 593, 601, 617, 631, 647, 653, 683, 691, 739, 751, 769, 773, 797, 811, 827, 829, 857

Offset: 1

Author

Tanya Khovanova, Oct 14 2007, Oct 17 2007, Nov 02 2007

Keywords

• nonn

Comments

The Mathematica coding uses the fact that the Pisano period - the period with which a Fibonacci sequence (mod n) repeats itself is not more than 6n and the fact that the Fibonacci sequence starts with 0.

Subsequence of A133246 except for 2.

Primes not in A155916. - Robert Israel, Nov 20 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A014437, A133246, A155916.

Programs

Maple

filter:= proc(p) local a,b,i;
  if not isprime(p) then return false fi;
  a:= 0: b:= 1;
for i from 2 do
  a,b:= b, (a+b) mod p;
  if b = 0 then
    if i mod 3 <> 0 then return false
    elif a = 1 then return true
    fi
  fi
od:
end proc:
select(filter, [2,seq(i,i=3..1000,2)]); # Robert Israel, Nov 20 2016

Mathematica

Transpose[ Select[Table[{Prime[m], Select[Table[{n, Mod[Fibonacci[n], Prime[m]]}, {n, 6Prime[m] + 1}], Mod[ #[[1]], 3] != 0 && #[[2]] == 0 &]}, {m, 300}], #[[2]] == {} &]][[1]]