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A088551
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Fibonacci winding number: the number of 'mod n' operations in one cycle of the Fibonacci sequence modulo n.
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2
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1, 3, 2, 8, 11, 7, 4, 11, 28, 3, 9, 12, 23, 19, 9, 16, 11, 7, 28, 5, 12, 23, 9, 48, 40, 35, 19, 4, 59, 12, 19, 15, 16, 39, 9, 36, 6, 27, 28, 19, 19, 43, 11, 59, 23, 15, 9, 55, 148, 35, 38, 52, 35, 6, 21, 31, 16, 26, 57, 28, 12, 21, 43, 68, 51, 67, 14, 19, 119, 32, 7, 72, 112, 99, 5, 33
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OFFSET
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2,2
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COMMENTS
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If pi(n) is the n-th Pisano number (A001175) then a(n) is usually about pi(n)/2 - and in any case a(n) > pi(n)/4.
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..10000
R. C. Johnson, Fibonacci Numbers and Resources.
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FORMULA
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n*a(n) = sum{k=1..A001175(n)} fibonacci(k) mod n. [From Mircea Merca, Jan 03 2011]
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EXAMPLE
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a(8)=4 because one cycle of the Fibonacci numbers modulo 8 is 0, 1, 1, 2, 3, 5; 0, 5, 5; 2, 7; 1; - including 4 'mod 8' operations, each marked with a semi-colon.
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CROSSREFS
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Cf. A001175, A015134, A214300.
Sequence in context: A209360 A095013 A094188 * A165660 A171634 A107300
Adjacent sequences: A088548 A088549 A088550 * A088552 A088553 A088554
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KEYWORD
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easy,nice,nonn
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AUTHOR
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R C Johnson (bob.johnson(AT)dur.ac.uk), Nov 19 2003
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EXTENSIONS
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More terms from T. D. Noe
Edited by Ray Chandler, Oct 26 2006
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STATUS
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approved
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