Search: id:A095791
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%I A095791
%S A095791 1,1,2,2,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,
%T A095791 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%U A095791 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9
%N A095791 Number of digits in lazy-Fibonacci-binary representation of n.
%C A095791 Here's how to form the lazy Fibonacci representation of n>=1. First, 
               define g(n) to be the Fibonacci number F(k-1), where k is the number 
               satisfying F(k)-1 <= n <= F(k+1)-2. Then let g(1)=g(n), g(2)=g(n-g(1)), 
               g(3)=g(n-g(1)-g(2)) and so on, until reaching h for which g(h) is 
               1 or 2. The desired representation is n = g(1)+g(2)+...+g(h).
%D A095791 P. Erdos and I. Joo, "On the Expansion of 1 = Sum{q^(-n_i)}," Period. 
               Math. Hung. 23 (1991), no. 1, 25-28. (This paper introduces lazy 
               Fibonacci representations.)
%H A095791 Vienna University of Technology, <a href="http://www.geometrie.tuwien.ac.at/
               steiner/lazy.pdf">The Joint Distribution of Greedy and Lazy Fibonacci 
               Expansions</a>.
%F A095791 1, 1, then F(3) 2's, then F(4) 3's, then F(5) 4's, ..., then F(k+1) k's, 
               ...
%F A095791 a(0)=a(1)=1 then a(n)=a(floor(n/tau))+1 where tau=(1+sqrt(5))/2 - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Dec 17 2006
%F A095791 a(n) = least k such that f^(k)(n)=0 where f^(k+1)(x)=f(f^(k)(x)) and 
               f(x)=floor(x/Phi) where Phi=(1+sqrt(5))/2 (see pari-gp program) - 
               Benoit Cloitre (benoit7848c(AT)orange.fr), May 24 2007
%e A095791 The lazy Fibonacci representation of 14 is 8+3+2+1, which in binary notation 
               is 10111, which consists of 5 digits.
%o A095791 (PARI) a(n)=if(n<2,1,a(floor(n*(-1+sqrt(5))/2))+1) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Dec 17 2006
%o A095791 (PARI) a(n)=if(n<0,0,c=1;s=n;while(floor(s*2/(1+sqrt(5)))>0,c++;s=floor(s*2/
               (1+sqrt(5))));c) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 
               24 2007
%Y A095791 Cf. A000045, A072649, A095792.
%Y A095791 Sequence in context: A085727 A143442 A137300 this_sequence A036042 A162988 
               A143824
%Y A095791 Adjacent sequences: A095788 A095789 A095790 this_sequence A095792 A095793 
               A095794
%K A095791 nonn
%O A095791 0,3
%A A095791 Clark Kimberling (ck6(AT)evansville.edu), Jun 05 2004

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