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

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

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