%I A020650
%S A020650 1,2,1,3,1,3,2,4,1,4,3,5,2,5,3,5,1,5,4,7,3,7,4,7,2,7,5,8,3,8,5,6,1,6,5,
               9,
%T A020650 4,9,5,10,3,10,7,11,4,11,7,9,2,9,7,12,5,12,7,11,3,11,8,13,5,13,8,7,1,7,
               6,
%U A020650 11,5,11,6,13,4,13,9,14,5,14,9,13,3,13,10,17,7,17,10,15,4,15,11,18,7,18
%N A020650 Numerators in recursive bijection from positive integers to positive 
               rationals (the bijection is f(1) = 1, f(2n) = f(n)+1, f(2n+1) = 1/
               (f(n)+1)).
%C A020650 The fractions are given in their reduced form, thus gcd(a(n), A020651(n)) 
               = 1 for all n. - Antti Karttunen (Antti.Karttunen(AT)iki.fi), May 
               26 2004
%H A020650 T. D. Noe, <a href="b020650.txt">Table of n, a(n) for n=1..10000</a>
%F A020650 a(1) = 1, a(2n) = a(n)+A020651(n), a(2n+1) = A020651(2n) = A020651(n) 
               - Antti Karttunen (Antti.Karttunen(AT)iki.fi), May 26 2004
%e A020650 1, 2, 1/2, 3, 1/3, 3/2, 2/3, 4, 1/4, 4/3, ...
%p A020650 A020650 := n -> `if`((n < 2),n, `if`(type(n,even), A020650(n/2)+A020651(n/
               2), A020651(n-1)));
%Y A020650 Cf. A020651.
%Y A020650 Bisection: A086592.
%Y A020650 Sequence in context: A144079 A071575 A038569 this_sequence A124224 A014599 
               A075825
%Y A020650 Adjacent sequences: A020647 A020648 A020649 this_sequence A020651 A020652 
               A020653
%K A020650 nonn,easy,frac,nice
%O A020650 1,2
%A A020650 David W. Wilson (davidwwilson(AT)comcast.net)