A133246 -id:A133246 - cp's OEIS frontend

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

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

nonn

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

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

Cf. A014437, A133246, A155916.

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

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]]

A137189 Numbers n such that no odd Fibonacci is divisible by n and n is not a multiple of another number in this sequence.

Original entry on oeis.org

2, 9, 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

Offset: 0

Tanya Khovanova, Mar 03 2008

nonn

Obviously if no odd Fibonacci is divisible by n, then no odd Fibonacci is divisible by a multiple of n.

The only composite in this sequence is 9.

			The most famous is the statement that no odd Fibonacci is divisible by 17.
Trivially, no odd Fibonacci is divisible by 2.

Tanya Khovanova 9 Divides no Odd Fibonacci

Cf. A133247 Prime numbers p with property that no odd Fibonacci number is divisible by p. A133246 Odd numbers n with property that no odd Fibonacci number is divisible by n.

cp's OEIS Frontend

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

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