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Search: id:A089911
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| 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Sequence has been applied by several composers to pitch structure in 12 tone equal temperament. The complete Fibonacci mod 12 system (a set of 10 periodic sequences) exhausts all possible ordered dyads; that is, every possible combination of two pitches is found in these sets.
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REFERENCES
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A. P. Shah, Fibonacci Sequence Modulo m, Fibonacci Quarterly, Vol. 6 (1968), pp. 139-141.
D. D. Wall, Fibonacci Series Modulo m, American Mathematical Monthly, Vol. 67 (1960), pp. 525-532.
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LINKS
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R. Knott, Fibonacci Numbers and the Golden Section
M. Renault, The Fibonacci Sequence Modulo M
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FORMULA
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Has period of 24, restricted period 12 and multiplier 5.
F(n) mod 12 = F(n-1) + F(n-2), F(0) = 0, F(1) = 1
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MAPLE
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with(combinat, fibonacci); A89911 := proc(n) fibonacci(n) mod 12; end;
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CROSSREFS
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Cf. A000045, A003893.
Adjacent sequences: A089908 A089909 A089910 this_sequence A089912 A089913 A089914
Sequence in context: A093086 A093092 A031111 this_sequence A098978 A111301 A096320
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KEYWORD
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nonn
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AUTHOR
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Casey Mongoven (cm(AT)caseymongoven.com), Nov 14 2003
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 15 2003
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