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A015134
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Consider Fibonacci-type sequences b(0)=X, b(1)=Y, b(k)=b(k-1)+b(k-2) mod n; all are periodic; sequence gives number of distinct periods.
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12
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1, 2, 2, 4, 3, 4, 4, 8, 5, 6, 14, 10, 7, 8, 12, 16, 9, 16, 22, 16, 29, 28, 12, 30, 13, 14, 14, 22, 63, 24, 34, 32, 39, 34, 30, 58, 19, 86, 32, 52, 43, 58, 22, 78, 39, 46, 70, 102, 25, 26, 42, 40, 27, 52, 160, 74, 63, 126, 62, 70, 63, 134, 104, 64, 57, 78, 34, 132, 101, 60, 74, 222
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OFFSET
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1,2
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COMMENTS
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b(k) >= k/4 (by counting zeros). - R C Johnson (bob.johnson(AT)dur.ac.uk), Nov 20 2003
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LINKS
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David Radcliffe, Table of n, a(n) for n = 1..1000
B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.8.5.
Jesse Fischer, Number Necklace Generator.
R. C. Johnson, Fibonacci Numbers and Resources.
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CROSSREFS
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Cf. A015135 (number of different orbit lengths of the 2-step recursion mod n), A106306 (primes that yield a simple orbit structure in 2-step recursions).
Sequence in context: A046701 A140472 A109168 * A171580 A246796 A177235
Adjacent sequences: A015131 A015132 A015133 * A015135 A015136 A015137
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KEYWORD
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nonn
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AUTHOR
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Phil Carmody
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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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STATUS
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approved
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