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A189768
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Irregular triangle in which row n contains the set of residues of the sequence Fibonacci(i) mod n for i=0,1,2,....
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6
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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
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OFFSET
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1,6
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COMMENTS
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Sequence A066853 gives the lengths of the rows. Sequence A079002 gives the n that have a complete set of residues.
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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}]]
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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