A189768 Irregular triangle in which row n contains the set of residues of the sequence Fibonacci(i) mod n for i=0,1,2,....

0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 5, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 5, 8, 10, 0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 0, 1, 2, 3, 5, 8, 10, 11, 12

Offset: 1

Author

T. D. Noe, May 10 2011

Keywords

• nonn
• tabf

Comments

Sequence A066853 gives the lengths of the rows. Sequence A079002 gives the n that have a complete set of residues.

Examples

			The triangle begins
0
0, 1
0, 1, 2
0, 1, 2, 3
0, 1, 2, 3, 4
0, 1, 2, 3, 4, 5
0, 1, 2, 3, 4, 5, 6
0, 1, 2, 3, 5, 7
0, 1, 2, 3, 4, 5, 6, 7, 8
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
		

Links

• T. D. Noe, Rows n = 1..100, flattened

Crossrefs

Cf. A000045 (Fibonacci numbers), A066853, A079002.

Programs

Mathematica

pisano[n_] := Module[{a = {1, 0}, a0, k = 0, s}, If[n == 1, 1, a0 = a; While[k++; s = Mod[Total[a], n]; a[[1]] = a[[2]]; a[[2]] = s; a != a0]; k]]; Flatten[Table[p=pisano[n]; f=Mod[Fibonacci[Range[0,p]],n]; Union[f], {n,15}]]