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A226081 Numerators in the Fibonacci (or rabbit) ordering of the positive rational numbers.

%I A226081 #23 Dec 01 2018 08:58:02
%S A226081 1,2,3,1,4,1,3,5,1,4,5,2,6,1,5,7,3,7,2,5,7,1,6,9,4,10,3,7,9,2,7,8,3,8,
%T A226081 1,7,11,5,13,4,9,13,3,10,11,4,11,2,9,12,5,11,3,8,9,1,8,13,6,16,5,11,
%U A226081 17,4,13,14,5,16,3,13,17,7,15,4,11,13,2,11,16
%N A226081 Numerators in the Fibonacci (or rabbit) ordering of the positive rational numbers.
%C A226081 See A226080.
%H A226081 Clark Kimberling, <a href="/A226081/b226081.txt">Table of n, a(n) for n = 1..6000</a>
%H A226081 <a href="/index/Fo#fraction_trees">Index entries for fraction trees</a>
%e A226081 The numerators are read from the rationals listed in "rabbit order":
%e A226081 1/1, 2/1, 3/1, 1/2, 4/1, 1/3, 3/2, 5/1, 1/4, 4/3, 5/2, 2/3, 6/1, ...
%t A226081 z = 13; d[s_List, t_List] := Part[s, Sort[Flatten[Map[Position[s, #] &, Complement[s, t]]]]]; g[1] = {1}; g[2] = {2}; Do[ g[n] = d[Riffle[g[n - 1] + 1, 1/g[n - 1]], g[n - 2]], {n, 3, z}];  (* Edited by _M. F. Hasler_, Nov 30 2018 *)
%t A226081 j[1] = g[1]; j[n_] := Join[j[n - 1], g[n]]; j[z];  (* rabbit-ordered rationals *)
%t A226081 Denominator[j[z]]   (* A226080 *)
%t A226081 Numerator[j[z]]     (* A226081 *)
%o A226081 (PARI) A226081_vec(N=100)={my(T=[1], S=T, A=T); while(N>#A=concat(A, apply(numerator, T=select(t->!setsearch(S, t), concat(apply(t->[t+1, 1/t], T))))), S=setunion(S, Set(T))); A} \\  _M. F. Hasler_, Nov 30 2018
%o A226081 (PARI) A226081(n)=numerator(RabbitOrderedRational(n)) \\ See A226080. - _M. F. Hasler_, Nov 30 2018
%Y A226081 Cf. A226080.
%K A226081 nonn,frac
%O A226081 1,2
%A A226081 _Clark Kimberling_, May 25 2013