A131341 Number of 0's in maximal Lucas representation (A130311) of n.

1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 0, 3, 3, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 0, 3, 3, 3, 2, 3, 3, 2, 2, 2, 2, 1, 3, 3, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 0, 4, 4, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3

Offset: 1

Author

Casey Mongoven, Jun 29 2007, corrected Mar 23 2008

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Ron Knott, Using the Fibonacci numbers to represent whole numbers.

Crossrefs

Cf. A131340, A000032, A102364.

Programs

Mathematica

lazy = Select[IntegerDigits[Range[400], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[#*Reverse@LucasL[Range[0, Length[#] - 1]]] & /@ lazy; Plus @@@ (1 - lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]) (* Amiram Eldar, Jul 05 2025 *)

Extensions

More terms from Amiram Eldar, Jul 05 2025