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Search: id:A015135
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| A015135 |
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Consider Fibonacci-type sequences f(0)=X, f(1)=Y, f(k)=f(k-1)+f(k-2) mod n; all are periodic; sequence gives number of distinct period lengths. |
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2
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| 1, 2, 2, 3, 3, 4, 2, 4, 3, 6, 3, 5, 2, 4, 5, 5, 2, 4, 3, 7, 3, 6, 2, 6, 4, 4, 4, 5, 3, 10, 3, 6, 5, 3, 5, 5, 2, 4, 4, 7, 2, 6, 2, 7, 7, 3, 2, 6, 3, 8, 4, 5, 2, 5, 5, 6, 5, 6, 3, 11, 2, 4, 5, 7, 5, 10, 2, 4, 3, 10, 3, 6, 2, 4, 7, 5, 5, 8, 3, 9, 5, 4, 2, 7, 5, 4, 5, 9, 2, 10, 4, 4, 5, 4, 7, 7, 2, 6, 7, 9, 3, 6, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Consider the 2-step recursion f(k)=f(k-1)+f(k-2) mod n. For any of the n^2 initial conditions f(1) and f(2) in Zn, the recursion has a finite period. Each of these n^2 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths for each n. For n=8, there are 4 different lengths: 1, 3, 6 and 12. The maximum possible length of an orbit is A001175(n), the period of the Fibonacci 2-step sequence mod n. - T. D. Noe (noe(AT)sspectra.com), May 02 2005
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LINKS
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Eric Weisstein's World of Mathematics, Fibonacci n-Step
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CROSSREFS
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Cf. A015134 (orbits of 2-step sequences), A106306 (primes that yield a simple orbit structure in 2-step recursions).
Sequence in context: A116370 A106486 A106494 this_sequence A116619 A091220 A057955
Adjacent sequences: A015132 A015133 A015134 this_sequence A015136 A015137 A015138
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KEYWORD
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nonn
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AUTHOR
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Phil Carmody (pc+oeis(AT)asdf.org)
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jan 06 2005
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