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A116543 Number of terms in greedy representation of n in terms of the Lucas numbers. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

I have been studying A007895 and similar sequences and created this sequence as an analog of A007895 for the Lucas sequence (A000032).

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

Ron Knott, Using the Fibonacci numbers to represent whole numbers.

FORMULA

Let L(N)=max(Lucas numbers < N). Then a(0)=0 a(N)=1+a(N-L(N)).

EXAMPLE

a(12)=2 because 12=11+1.

MATHEMATICA

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 *)

CROSSREFS

Cf. A131343, A000032, A007895.

Sequence in context: A080757 A037196 A169818 * A256911 A107260 A279346

Adjacent sequences:  A116540 A116541 A116542 * A116544 A116545 A116546

KEYWORD

nonn

AUTHOR

James E Davis, Mar 28 2006, Jun 07 2006

EXTENSIONS

Edited by N. J. A. Sloane, Aug 10 2007

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)