This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A189768 #6 Mar 30 2012 17:22:58 %S A189768 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, %T A189768 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, %U A189768 9,10,11,0,1,2,3,5,8,10,11,12 %N A189768 Irregular triangle in which row n contains the set of residues of the sequence Fibonacci(i) mod n for i=0,1,2,.... %C A189768 Sequence A066853 gives the lengths of the rows. Sequence A079002 gives the n that have a complete set of residues. %H A189768 T. D. Noe, <a href="/A189768/b189768.txt">Rows n = 1..100, flattened</a> %e A189768 The triangle begins %e A189768 0 %e A189768 0, 1 %e A189768 0, 1, 2 %e A189768 0, 1, 2, 3 %e A189768 0, 1, 2, 3, 4 %e A189768 0, 1, 2, 3, 4, 5 %e A189768 0, 1, 2, 3, 4, 5, 6 %e A189768 0, 1, 2, 3, 5, 7 %e A189768 0, 1, 2, 3, 4, 5, 6, 7, 8 %e A189768 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 %t A189768 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}]] %Y A189768 Cf. A000045 (Fibonacci numbers), A066853, A079002. %K A189768 nonn,tabf %O A189768 1,6 %A A189768 _T. D. Noe_, May 10 2011