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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 (list; graph; refs; listen; history; text; internal format)
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];  (* rabbit-ordered 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

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)