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If one lines up the columns of the binary representations in A130310, the minimal (or "greedy") Lucas representation of n, this sequence gives the column number (starting with 0) of the starting point of the blocks of 1s which occur.
0

%I #7 Jan 05 2025 19:51:39

%S 1,0,2,3,1,0,4,1,0,2,5,1,0,2,3,1,0,6,1,0,2,3,1,0,4,1,0,2,7,1,0,2,3,1,

%T 0,4,1,0,2,5,1,0,2,3,1,0,8,1,0,2,3,1,0,4,1,0,2,5,1,0,2,3,1,0,6,1,0,2,

%U 3,1,0,4,1,0,2,9

%N If one lines up the columns of the binary representations in A130310, the minimal (or "greedy") Lucas representation of n, this sequence gives the column number (starting with 0) of the starting point of the blocks of 1s which occur.

%H C. Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/33-1/kimberling.pdf">The Zeckendorf array equals the Wythoff array</a>, Fibonacci Quarterly 33 (1995) 3-8.

%Y Cf. A130310, A035614.

%K nonn

%O 1,3

%A _Casey Mongoven_, May 23 2010