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Search: id:A073334
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| A073334 |
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The so-called "rhythmic infinity system" of Danish composer Per Noergaard. |
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1
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| 3, 5, 8, 5, 8, 13, 8, 5, 8, 13, 21, 13, 8, 13, 8, 5, 8, 13, 21, 13, 21, 34, 21, 13, 8, 13, 21, 13, 8, 13, 8, 5, 8, 13, 21, 13, 21, 34, 21, 13, 21, 34, 55, 34, 21, 34, 21, 13, 8, 13, 21, 13, 21, 34, 21, 13, 8, 13, 21, 13, 8, 13, 8, 5, 8, 13, 21, 13, 21, 34, 21, 13, 21, 34, 55, 34, 21
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
Erling Kullberg, Beyond infinity: on the infinity series - the DNA of hierarchical music, in Anders Beyer, ed., The Music of Per Noergaard: Fourteen Interpretive Essays, Scolar Press, 1996, pp. 71-93.
Jeffrey Shallit, The mathematics of Per Noergaard's rhythmic infinity system, Fib. Q., 43 (2005), 262-268.
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LINKS
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J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II
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FORMULA
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a(n) = F(c(n)+4) where c(n) counts the blocks of consecutive identical symbols in the binary expansion of n and F() is the Fibonacci sequence.
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EXAMPLE
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a(5) = 13 since there are 3 blocks of consecutive identical systems in the binary expansion of 5 (namely, 101), 4+3 = 7, and the 7-th Fibonacci number is 13.
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CROSSREFS
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Cf. A005811, A000045.
Sequence in context: A020864 A021902 A136188 this_sequence A021740 A110641 A121729
Adjacent sequences: A073331 A073332 A073333 this_sequence A073335 A073336 A073337
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KEYWORD
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nonn
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AUTHOR
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Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca), Aug 25 2002
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