A133246 Odd numbers n with property that no odd Fibonacci number is divisible by n.

9, 17, 19, 23, 27, 31, 45, 51, 53, 57, 61, 63, 69, 79, 81, 83, 85, 93, 95, 99, 107, 109, 115, 117, 119, 133, 135, 137, 153, 155, 159, 161, 167, 171, 173, 181, 183, 187, 189, 197, 207, 209, 211, 217, 221, 225, 227, 229, 237, 241, 243, 247, 249, 253, 255, 257, 261

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.

Links

Table of n, a(n) for n=1..57.

Tanya Khovanova, 9 Divides no Odd Fibonacci, arXiv:0712.3509 [math.CO], 2007.

Mathematica

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]]

Crossrefs

Cf. A133247.

Sequence in context: A364540 A347250 A192049 * A190151 A144752 A317332

Adjacent sequences: A133243 A133244 A133245 * A133247 A133248 A133249

Keyword

nonn

Author

Tanya Khovanova, Oct 14 2007, Oct 17 2007

Status

approved