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Search: id:A001176
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| A001176 |
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Number of zeros in fundamental period of Fibonacci numbers mod n.
(Formerly M0165 N0064)
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+0
12
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| 1, 1, 2, 1, 4, 2, 2, 2, 2, 4, 1, 2, 4, 2, 2, 2, 4, 2, 1, 2, 2, 1, 2, 2, 4, 4, 2, 2, 1, 2, 1, 2, 2, 4, 2, 2, 4, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 1, 1, 2, 4, 1, 2, 2, 4, 2, 2, 2, 2, 2, 1, 2, 4, 4, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 1, 2, 2, 2, 2
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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If the Fibonacci numbers are indexed so that 3 is the fourth number, then if the modulo base is a Fibonacci number (>= 3) with an even index, the period has 2 zeros. If the base is a Fibonacci number (>= 5) with an odd index, the period has 4 zeros. - Kerry Mitchell (lkmitch(AT)gmail.com), Dec 11 2005
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REFERENCES
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J. D. Fulton and W. L. Morris, On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica, 16 (1969), 105-110.
B. H. Hannon and W. L. Morris, Tables of Arithmetical Functions Related to the Fibonacci Numbers. Report ORNL-4261, Oak Ridge National Laboratory, Oak Ridge, Tennessee, Jun 1968.
Review of B. H. Hannon and W. L. Morris tables, Math. Comp., 23 (1969), 459-460.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
M. Renault, Fibonacci sequence modulo m
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FORMULA
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a(n) = A001175(n)/A001177(n) for n >= 1.
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EXAMPLE
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{F(n) mod 1} has fundamental period (0) with 1 zero.
{F(n) mod 2} has fundamental period (0,1,1) with 1 zero.
{F(n) mod 3} has fundamental period (0,1,1,2,0,2,2,1) with 2 zeros.
{F(n) mod 4} has fundamental period (0,1,1,2,3,1), with 1 zero.
{F(n) mod 5} has fundamental period (0,1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,2,2,4,1) with 4 zeros.
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CROSSREFS
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Cf. A001175, A001177, A053027, A053028, A053029, A053030, A053031, A053032.
Sequence in context: A109090 A080100 A161822 this_sequence A136693 A086685 A094571
Adjacent sequences: A001173 A001174 A001175 this_sequence A001177 A001178 A001179
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better description and more terms from Henry Bottomley (se16(AT)btinternet.com), Feb 01 2000. Examples from David W. Wilson, Jan 05 2005.
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