A116543 Number of terms in greedy representation of n in terms of the Lucas numbers.

0, 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

Offset

0,6

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 = 0..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)).

a(n) = A007953(A130310(n)). - Amiram Eldar, Feb 17 2022

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. A000032, A007895, A007953, A130310, A131343.

Sequence in context: A368594 A169818 A367816 * A256911 A347562 A359790

Adjacent sequences: A116540 A116541 A116542 * A116544 A116545 A116546

Keyword

nonn,base

Author

James E Davis, Mar 28 2006, Jun 07 2006

Extensions

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

a(0) added by Amiram Eldar, Feb 17 2022

Status

approved