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A116543
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Number of terms in greedy representation of n in terms of the Lucas numbers.
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5
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1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 3, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 4, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 4, 2, 3, 3, 3, 3, 4, 4, 3, 4, 4, 4, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 4, 2, 3, 3, 3, 3, 4, 4, 3, 4, 4, 4, 2
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OFFSET
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1,5
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COMMENTS
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I have been studying A007895 and similar sequences and created this sequence as an analog of A007895 for the Lucas sequence (A000032).
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..10000
Ron Knott, Using the Fibonacci numbers to represent whole numbers.
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FORMULA
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Let L(N)=max(Lucas numbers < N). Then a(0)=0 a(N)=1+a(N-L(N)).
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EXAMPLE
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a(12)=2 because 12=11+1.
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MATHEMATICA
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s = Reverse[Sort[Table[LucasL[n - 1], {n, 1, 22}]]];
t = Map[Length[Select[Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, s]][[2, 1]], # > 0 &]] &, Range[1000]] (* Peter J. C. Moses, Oct 18 2012 *)
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CROSSREFS
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Cf. A131343, A000032, A007895.
Sequence in context: A080757 A037196 A169818 * A256911 A107260 A279346
Adjacent sequences: A116540 A116541 A116542 * A116544 A116545 A116546
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KEYWORD
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nonn
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AUTHOR
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James E Davis, Mar 28 2006, Jun 07 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, Aug 10 2007
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STATUS
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approved
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