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A118965
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Number of missing residues in Fibonacci sequence mod n.
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2
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0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 1, 4, 0, 0, 5, 4, 7, 7, 0, 12, 8, 4, 11, 0, 8, 0, 7, 19, 0, 12, 11, 14, 21, 0, 21, 8, 25, 14, 10, 22, 24, 10, 24, 0, 25, 32, 33, 12, 0, 16, 22, 16, 25, 43, 31, 24, 38, 22, 5, 36, 41, 40, 22, 20, 28, 16, 48, 40, 0, 27, 57
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OFFSET
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1,8
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COMMENTS
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If n belongs to A079002, then a(n) = 0. - Michel Marcus, May 27 2013
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REFERENCES
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Author?, Crux Mathematicorum, Fibonacci Residues, 1997 Vol. 23 No. 4 pp. 224-6 CMS.
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly (67 #6, Jun-Jul 1960), pp. 525-532.
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LINKS
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Table of n, a(n) for n=1..72.
Cyrus Hsia et al., Mathematical Mayhem Editors, Fibonacci residues, Crux Mathematicorum 23:4 pp. 224-226.
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly (67 #6, Jun-Jul 1960), pp. 525-532.
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FORMULA
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a(n) = n - A066853(n). - Michel Marcus, May 27 2013
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EXAMPLE
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The Fibonacci sequence mod 8 is { 0 1 1 2 3 5 0 5 5 2 7 1 0 1 1 ... } - a periodic sequence with a period of 12 (see A001175). Two residues do not occur in this sequence (4 and 6), therefore a(8) = 2.
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CROSSREFS
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Cf. A066853, A001175.
Sequence in context: A136334 A155039 A106235 * A121552 A158118 A212137
Adjacent sequences: A118962 A118963 A118964 * A118966 A118967 A118968
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KEYWORD
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nonn
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AUTHOR
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Casey Mongoven, May 07 2006
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EXTENSIONS
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Index corrected by Michel Marcus, May 27 2013
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STATUS
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approved
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