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Search: id:A112310
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| A112310 |
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Number of terms in lazy Fibonacci representation of n. |
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+0
3
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| 0, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 5, 3, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 5, 6, 4, 4, 5, 4, 5, 5, 5, 6, 4, 5, 5, 5, 6, 5, 5, 6, 5, 6, 6, 6, 7, 4, 5, 5, 5, 6, 5, 5, 6, 5, 6, 6, 6, 7, 5, 5, 6, 5, 6, 6, 6, 7, 5, 6, 6, 6, 7, 6, 6, 7, 6, 7, 7, 7, 8, 5, 5, 6, 5, 6, 6, 6, 7, 5, 6, 6, 6, 7, 6, 6, 7, 6
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Equivalently, the number of ones in the maximal Fibonacci bit-representation (A104326) of n.
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REFERENCES
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J. L. Brown, A New Characterization of the Fibonacci Numbers, Fibonacci Quarterly, 3 (1965), pp. 1-8.
W. Steiner, The joint distribution of greedy and lazy Fibonacci expansions, Fib. Q., 43 (No. 1, 2005), 60-69.
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LINKS
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Ron Knott, Using the Fibonacci numbers to represent whole numbers.
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EXAMPLE
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a(10) = 3 because A104326(10) = 1110 contains three ones.
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CROSSREFS
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Number of terms in row n of A112309. Cf. A117479, A035517, A104326, A007895.
Record positions are in A001911. (Ray Chandler).
Sequence in context: A104307 A128330 A133801 this_sequence A137734 A078705 A050331
Adjacent sequences: A112307 A112308 A112309 this_sequence A112311 A112312 A112313
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 01 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 01 2005
Merged with a sequence from Casey Mongoven (cm(AT)caseymongoven.com), Mar 20 2006, by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 19 2006
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