A133246 - OEIS

%I #7 Jan 01 2019 20:14:44

%S 9,17,19,23,27,31,45,51,53,57,61,63,69,79,81,83,85,93,95,99,107,109,

%T 115,117,119,133,135,137,153,155,159,161,167,171,173,181,183,187,189,

%U 197,207,209,211,217,221,225,227,229,237,241,243,247,249,253,255,257,261

%N Odd numbers n with property that no odd Fibonacci number is divisible by n.

%C 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.

%H Tanya Khovanova, <a href="https://arxiv.org/abs/0712.3509">9 Divides no Odd Fibonacci</a>, arXiv:0712.3509 [math.CO], 2007.

%t Transpose[ Select[Table[{k, Select[Table[{n, Mod[Fibonacci[n], k]}, {n, 6k + 1}], Mod[ #[[1]], 3] != 0 && #[[2]] == 0 &]}, {k, 1, 351, 2}], #[[2]] == {} &]][[1]]

%Y Cf. A133247.

%K nonn

%O 1,1

%A _Tanya Khovanova_, Oct 14 2007, Oct 17 2007