%I A071912
%S A071912 0,1,1,2,1,3,2,3,1,4,3,4,1,5,4,5,3,5,2,5,1,6,5,6,1,7,6,7,5,7,4,7,3,
%T A071912 7,2,7,1,8,7,8,5,8,3,8,1,9,8,9,7,9,5,9,4,9,2,9,1,10,9,10,7,10,3,10,
%U A071912 1,11,10,11,9,11,8,11,7,11,6,11,5,11,4,11,3,11,2,11,1,12,11,12,7,12
%N A071912 a(0) = 0, a(1) = 1; to get a(n+1) for n >= 1, let m = a(n) and consider 
               in turn the numbers k = m-1, m-2, ..., 2, 1, m+1, m+2, m+3, ... until 
               reach a k such that GCD(m,k) = 1 and m/k is different from all a(i)/
               a(i+1) for i = 0, ...,n-1.
%C A071912 A version of a greedy construction of an integer-valued function a such 
               that a(n)/a(n+1) runs through all nonnegative rationals exactly once.
%C A071912 After initial 0, odd-indexed terms are integers in order with m repeated 
               phi(m) times; even-indexed terms are the corresponding numbers <= 
               m and relatively prime to m, in descending order. - Franklin T. Adams-Watters 
               (FrankTAW(AT)Netscape.net), Dec 06 2006
%H A071912 N. J. A. Sloane, <a href="a071912.txt">FORTRAN program</a>
%e A071912 After [0 1 1 2 1 3 2] we have seen the fractions 0/1, 1/1, 1/2, 2/1, 
               1/3, 3/2; we consider k = 1, 3, 4, 5, ...; the first of these that 
               gives a new ratio is k=3, giving 2/3, so the next term is 3.
%Y A071912 Cf. A002487.
%Y A071912 Bisections: A038567 and essentially A020653.
%Y A071912 Sequence in context: A097285 A057432 A038568 this_sequence A070940 A020651 
               A160232
%Y A071912 Adjacent sequences: A071909 A071910 A071911 this_sequence A071913 A071914 
               A071915
%K A071912 nonn,easy,nice
%O A071912 0,4
%A A071912 N. J. A. Sloane (njas(AT)research.att.com), Jun 13 2002