A130311 Maximal (or "lazy") Lucas representation of n. Binary system for representing integers using Lucas numbers (A000032) as a base.

0, 10, 1, 11, 110, 101, 111, 1011, 1110, 1101, 1111, 10110, 10101, 10111, 11011, 11110, 11101, 11111, 101011, 101110, 101101, 101111, 110110, 110101, 110111, 111011, 111110, 111101, 111111, 1010110, 1010101, 1010111, 1011011, 1011110, 1011101, 1011111, 1101011, 1101110

Offset: 0

Author

Casey Mongoven, May 21 2007; corrected Mar 23 2008

Keywords

• nonn
• base

Examples

			a(7) = 1110 because 4 + 3 + 1 = 8.
a(8) = 1101 because 4 + 3 + 2 = 9.
		

References

• Edouard Zeckendorf, Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège, Vol. 41 (1972), pp. 179-182.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Ron Knott, Using Fibonacci Numbers to Represent Whole Numbers.

Crossrefs

Cf. A000032, A104326, A130310, A131343.

Programs

Mathematica

lazy = Select[IntegerDigits[Range[10^2], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[# * Reverse@LucasL[Range[0, Length[#] - 1]]] & /@ lazy; Join[{0}, FromDigits /@ lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]] (* Amiram Eldar, Feb 17 2022 *)

Extensions

a(0) and more terms from Amiram Eldar, Feb 17 2022