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

1,1

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

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]]

Crossrefs

Cf. A014437, A133246, A155916.

Sequence in context: A038980 A074857 A191018 * A216965 A145100 A145101

Adjacent sequences: A133244 A133245 A133246 * A133248 A133249 A133250

Keyword

nonn

Author

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

Status

approved