

A104325


Number of runs of equal bits in the Dual Zeckendorf (binary) representation of n.


2



1, 2, 1, 3, 2, 1, 4, 3, 3, 2, 1, 5, 4, 3, 4, 3, 3, 2, 1, 6, 5, 5, 4, 3, 5, 4, 3, 4, 3, 3, 2, 1, 7, 6, 5, 6, 5, 5, 4, 3, 6, 5, 5, 4, 3, 5, 4, 3, 4, 3, 3, 2, 1, 8, 7, 7, 6, 5, 7, 6, 5, 6, 5, 5, 4, 3, 7, 6, 5, 6, 5, 5, 4, 3, 6, 5, 5, 4, 3, 5, 4, 3, 4, 3, 3, 2, 1, 9, 8, 7, 8, 7, 7, 6, 5, 8, 7, 7, 6, 5
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OFFSET

1,2


COMMENTS

Sequence has some interesting fractal properties (plot it!)


LINKS

Table of n, a(n) for n=1..100.
Ron Knott using Fibonacci Numbers to represent whole numbers
Casey Mongoven, Sonification of multiple Fibonaccirelated sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175192.


EXAMPLE

The Dual Zeckendorf representation of 13 is 10110(fib) corresponding to {8, 3, 2}
The largest set of Fibonacci numbers whose sum is n (cf. the Zeckendorf rep is the smallest set). This is composed of runs of one 1, one 0, two 1's, one 0 i.e. 4 runs in all so a(13)=4


MAPLE

dualzeckrep:=proc(n)local i, z; z:=zeckrep(n); i:=1; while i<=nops(z)2 do if z[i]=1 and z[i+1]=0 and z[i+2]=0 then z[i]:=0; z[i+1]:=1; z[i+2]:=1; if i>3 then i:=i2 fi else i:=i+1 fi od; if z[1]=0 then z:=subsop(1=NULL, z) fi; z end proc: countruns:=proc(s)local i, c, elt; elt:=s[1]; c:=1; for i from 2 to nops(s) do if s[i]<>s[i1] then c:=c+1 fi od; c end proc: seq(countruns(dualzeckrep(n)), n=1..100);


CROSSREFS

Cf. A014417, A104324.
Sequence in context: A212536 A188277 A135227 * A204925 A133084 A118851
Adjacent sequences: A104322 A104323 A104324 * A104326 A104327 A104328


KEYWORD

nonn,hear


AUTHOR

Ron Knott, Mar 01 2005


STATUS

approved



