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

%I A133247 #9 Nov 21 2016 04:18:46
%S A133247 2,17,19,23,31,53,61,79,83,107,109,137,167,173,181,197,211,227,229,
%T A133247 241,257,271,293,317,349,379,383,409,421,439,443,467,499,503,541,571,
%U A133247 587,593,601,617,631,647,653,683,691,739,751,769,773,797,811,827,829,857
%N A133247 Prime numbers p with property that no odd Fibonacci number is divisible by p.
%C A133247 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.
%C A133247 Subsequence of A133246 except for 2.
%C A133247 Primes not in A155916. - _Robert Israel_, Nov 20 2016
%H A133247 Robert Israel, <a href="/A133247/b133247.txt">Table of n, a(n) for n = 1..2000</a>
%p A133247 filter:= proc(p) local a,b,i;
%p A133247   if not isprime(p) then return false fi;
%p A133247   a:= 0: b:= 1;
%p A133247 for i from 2 do
%p A133247   a,b:= b, (a+b) mod p;
%p A133247   if b = 0 then
%p A133247     if i mod 3 <> 0 then return false
%p A133247     elif a = 1 then return true
%p A133247     fi
%p A133247   fi
%p A133247 od:
%p A133247 end proc:
%p A133247 select(filter, [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Nov 20 2016
%t A133247 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]]
%Y A133247 Cf. A014437, A133246, A155916.
%K A133247 nonn
%O A133247 1,1
%A A133247 _Tanya Khovanova_, Oct 14 2007, Oct 17 2007, Nov 02 2007