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

0,2

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.

Example

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

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 *)

Crossrefs

Cf. A000032, A104326, A130310, A131343.

Sequence in context: A164899 A164844 A287015 * A063672 A070606 A332803

Adjacent sequences: A130308 A130309 A130310 * A130312 A130313 A130314

Keyword

nonn,base

Author

Casey Mongoven, May 21 2007; corrected Mar 23 2008

Extensions

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

Status

approved