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

0,4

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Ron Knott, Using the Fibonacci numbers to represent whole numbers.

Formula

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

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 *)

Crossrefs

Cf. A000032, A007895, A130311, A116543.

Sequence in context: A048689 A069923 A095840 * A089051 A364631 A331255

Adjacent sequences: A131340 A131341 A131342 * A131344 A131345 A131346

Keyword

nonn,base

Author

Casey Mongoven, Jun 29 2007

Extensions

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

Status

approved