%I A135817
%S A135817 1,1,2,3,2,4,3,3,5,4,4,4,3,6,5,5,5,4,5,4,4,7,6,6,6,5,6,5,5,6,5,5,5,4,8,
%T A135817 7,7,7,6,7,6,6,7,6,6,6,5,7,6,6,6,5,6,5,5,9,8,8,8,7,8,7,7,8,7,7,7,6,8,7,
%U A135817 7,7,6,7,6,6,8,7,7,7,6,7,6,6,7,6,6,6,5,10,9,9,9,8,9,8,8,9,8,8,8,7,9,8,
               8
%N A135817 Length of Wythoff representation of n.
%C A135817 For the Wythoff representation of n see the W. Lang reference.
%C A135817 The Wythoff complemenatry sequences are A(n):=A000201(n) and B(n)=A001950(n), 
               n> =1. The Wythoff representation of n=1 is A(1) and for n>=2 there 
               is a unique representation as composition of A- or B-sequence applied 
               to B(1)=2. E.g. n=4 is A(A(B(1))), written as AAB or as `110`, i.e. 
               1 for A and 0 for B.
%C A135817 The Wythoff orbit of 1 (starting always with B(1), applying any number 
               of A- or B-sequences) produces every number n>1 just once. This produces 
               a binary Wythoff code for n>1, ending always in 0 (for B(1)). See 
               the W. Lang link for this code.
%D A135817 W. Lang, The Wythoff and the Zeckendorf representations of numbers are 
               equivalent, in G. E. Bergum et al. (edts.) Application of Fibonacci 
               numbers vol. 6, Kluwer, Dordrecht, 1996, pp.319-337.
%H A135817 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A135817.text"> 
               Wythoff representations for n=1...150. </a>
%F A135817 a(n) = number of digits in Wythoff representation of n>=1.
%F A135817 a(n) = length of Wythoff code for n>=1.
%F A135817 a(n) = number of applications of Wythoff sequences A or B on 1 in the 
               Wythoff representation for n >=1.
%e A135817 W(4) = `110`, i.e. 4 = A(A(B(1))) with Wythoff's A and B sequences.
%Y A135817 Cf. A135818 (number of 1's or A's in Wythoff representation of n).
%Y A135817 Cf. A007895 (number of 0's or B's in Wythoff representation of n).
%Y A135817 Sequence in context: A089215 A070296 A072645 this_sequence A122060 A088939 
               A004596
%Y A135817 Adjacent sequences: A135814 A135815 A135816 this_sequence A135818 A135819 
               A135820
%K A135817 nonn,easy
%O A135817 1,3
%A A135817 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jan 21 2008, 
               Feb 22 2008, May 21 2008, Sep 08 2008