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Search: id:A106287
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| A106287 |
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Number of orbits of the 5-step recursion mod n. |
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5
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| 1, 8, 5, 96, 5, 56, 7, 1468, 203, 40, 11, 1312, 13, 56, 25, 23400, 17, 6392, 193, 480, 35, 88, 555, 37180, 2505, 104, 15539, 672, 293, 280, 151, 374292, 55, 136, 35, 199744, 37, 6128, 65, 7340, 41, 392, 1899, 1056, 1015, 6648, 313775, 627280, 14413, 20040, 85
(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 5-step recursion x(k)=x(k-1)+x(k-2)+x(k-3)+x(k-4)+x(k-5) mod n. For any of the n^5 initial conditions x(1), x(2), x(3), x(4) and x(5) in Zn, the recursion has a finite period. Each of these n^5 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths (A106290). For instance, the 1468 orbits mod 8 have lengths of 1, 2, 3, 6, 12 and 24.
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REFERENCES
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D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, Vol. 67, 1960, 525-532.
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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 Fibonacci sequences), A106285 (orbits of 3-step sequences), A106286 (orbits of 4-step sequences), A106290 (number of different orbit lengths), A106309 (n producing a simple orbit structure).
Sequence in context: A070484 A096480 A038283 this_sequence A010117 A010119 A010116
Adjacent sequences: A106284 A106285 A106286 this_sequence A106288 A106289 A106290
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 02 2005
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