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A116543
Number of terms in greedy representation of n in terms of the Lucas numbers.
17
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).
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
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