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Search: id:A083368
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| A083368 |
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A Fibbinary system represents a number as a sum of distinct Fibonacci numbers (instead of distinct powers of two). Using representations without adjacent zeros, a(n) = the highest bit-position which changes going from n-1 to n. |
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2
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| 1, 2, 1, 3, 2, 1, 4, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 6, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 7, 2, 1, 4, 1, 3, 2, 1, 6, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 8, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 7, 2, 1, 4, 1, 3, 2, 1, 6, 1, 3, 2, 1, 5, 2, 1, 4, 1, 3, 2, 1, 9, 2, 1, 4, 1, 3, 2, 1, 6, 1, 3, 2, 1, 5, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A003754(n), when written in binary, is the representation of n.
Often one uses Fibbinary representations without adjacent ones (the Zeckendorf expansion).
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REFERENCES
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Jay Kappraff, Beyond Measure: A Guided Tour Through Nature, Myth and Number, World Scientific, 2002, page 460.
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FORMULA
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For n = F(a)-1 to F(a+1)-2, a(n) = A035612(F(a+1)-1-n).
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EXAMPLE
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27 is represented 110111, 28 is 111010; the fourth position changes, so a(28)=4.
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CROSSREFS
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A035612 is the analogous sequence for Zeckendorf representations.
A001511 is the analogous sequence for power-of-two representations.
Cf. A001511, A003714, A003754, A035612.
Sequence in context: A138530 A002341 A128260 this_sequence A112379 A073932 A082404
Adjacent sequences: A083365 A083366 A083367 this_sequence A083369 A083370 A083371
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 04 2003
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Nov 12 2005
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