This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A226212 Zeckendorf distance between n and floor(n/2). 3
 1, 1, 2, 1, 2, 1, 3, 4, 4, 3, 5, 5, 4, 6, 6, 5, 5, 7, 7, 7, 6, 8, 8, 8, 8, 7, 7, 7, 9, 9, 9, 9, 9, 8, 8, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 11, 11, 11, 11, 11, 11, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Zeckendorf distance is defined at A226207. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 EXAMPLE 11 = 8 + 3 -> 5 + 2 -> 3 + 1 -> 2, and 5 -> 3 -> 2.  The total number of Zeckendorf downshifts (i.e., arrows) is 5, so that a(11) = D(11,5) = 5. MATHEMATICA zeck[n_Integer] := Block[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, z = {}},    While[k > 1, If[t >= Fibonacci[k], AppendTo[z, 1]; t = t - Fibonacci[k], AppendTo[z, 0]]; k--]; If[n > 0 && z[[1]] == 0, Rest[z], z]]; d[n1_, n2_] := Module[{z1 = zeck[n1], z2 = zeck[n2]}, Length[z1] + Length[z2] - 2 (NestWhile[# + 1 &, 1, z1[[#]] == z2[[#]] &, 1, Min[{Length[z1], Length[z2]}]] - 1)]; lst = Map[d[#, Floor[#/2]] &, Range[100]] (* Peter J. C. Moses, May 30 2013 *) CROSSREFS Cf. A226080, A226207, A226211. Sequence in context: A133117 A210850 A051276 * A233439 A256600 A137752 Adjacent sequences:  A226209 A226210 A226211 * A226213 A226214 A226215 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 31 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)