Search: id:A135817 Results 1-1 of 1 results found. %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, Wythoff representations for n=1...150. %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 Search completed in 0.002 seconds