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

%I A116543 #29 Feb 17 2022 09:59:49
%S A116543 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,
%T A116543 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,
%U A116543 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
%N A116543 Number of terms in greedy representation of n in terms of the Lucas numbers.
%C A116543 I have been studying A007895 and similar sequences and created this sequence as an analog of A007895 for the Lucas sequence (A000032).
%H A116543 Clark Kimberling, <a href="/A116543/b116543.txt">Table of n, a(n) for n = 0..10000</a>
%H A116543 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrep.html">Using the Fibonacci numbers to represent whole numbers</a>.
%F A116543 Let L(n) = max(Lucas numbers < n). Then a(0) = 0, a(n) = 1 + a(n-L(n)).
%F A116543 a(n) = A007953(A130310(n)). - _Amiram Eldar_, Feb 17 2022
%e A116543 a(12)=2 because 12=11+1.
%t A116543 s = Reverse[Sort[Table[LucasL[n - 1], {n, 1, 22}]]];
%t A116543 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 *)
%Y A116543 Cf. A000032, A007895, A007953, A130310, A131343.
%K A116543 nonn,base
%O A116543 0,6
%A A116543 _James E Davis_, Mar 28 2006, Jun 07 2006
%E A116543 Edited by _N. J. A. Sloane_, Aug 10 2007
%E A116543 a(0) added by _Amiram Eldar_, Feb 17 2022