

A226081


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


4



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, 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, 17, 4, 13, 14, 5, 16, 3, 13, 17, 7, 15, 4, 11, 13, 2, 11, 16
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OFFSET

1,2


COMMENTS

See A226080.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..6000
Index entries for fraction trees


EXAMPLE

The numerators are read from the rationals listed in "rabbit order":
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, ...


MATHEMATICA

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 *)
j[1] = g[1]; j[n_] := Join[j[n  1], g[n]]; j[z]; (* rabbitordered rationals *)
Denominator[j[z]] (* A226080 *)
Numerator[j[z]] (* A226081 *)


PROG

(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
(PARI) A226081(n)=numerator(RabbitOrderedRational(n)) \\ See A226080.  M. F. Hasler, Nov 30 2018


CROSSREFS

Cf. A226080.
Sequence in context: A199539 A089555 A098554 * A109201 A002946 A286477
Adjacent sequences: A226078 A226079 A226080 * A226082 A226083 A226084


KEYWORD

nonn,frac


AUTHOR

Clark Kimberling, May 25 2013


STATUS

approved



