A131343 Number of 1's in maximal Lucas representation (A130311) of n.

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 6, 4, 4, 5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, 6, 6, 6, 6, 7, 5, 5, 5, 6, 5, 5, 6, 6, 6, 6, 7, 5, 5, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 7, 7, 7, 8, 5, 5, 6, 6, 6, 6, 7, 6, 6, 6, 7

Offset: 0

Author

Casey Mongoven, Jun 29 2007

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Ron Knott, Using the Fibonacci numbers to represent whole numbers.

Crossrefs

Cf. A000032, A007895, A130311, A116543.

Programs

Mathematica

lazy = Select[IntegerDigits[Range[400], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[# * Reverse@LucasL[Range[0, Length[#] - 1]]] & /@ lazy; Join[{0}, Plus@@@ lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]] (* Amiram Eldar, Feb 17 2022 *)

Formula

a(n) = A007953(A130311(n)). - Amiram Eldar, Feb 17 2022

Extensions

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