A380443 a(n) = numerator(b(n)), where b(n) = b(n/2)/2 for n even and 1 - b((n-1)/2)/2 for n odd with b(1) = 1.

1, 1, 1, 1, 3, 1, 3, 1, 7, 3, 5, 1, 7, 3, 5, 1, 15, 7, 9, 3, 13, 5, 11, 1, 15, 7, 9, 3, 13, 5, 11, 1, 31, 15, 17, 7, 25, 9, 23, 3, 29, 13, 19, 5, 27, 11, 21, 1, 31, 15, 17, 7, 25, 9, 23, 3, 29, 13, 19, 5, 27, 11, 21, 1, 63, 31, 33, 15, 49, 17, 47, 7, 57, 25, 39

Offset

1,5

Links

Stefano Spezia, Table of n, a(n) for n = 1..10000

John M. Campbell, A generalization of Deterministic Finite Automata related to discharging, arXiv:2506.14072 [cs.FL], 2025. See pp. 6-7.

Example

1/1, 1/2, 1/2, 1/4, 3/4, 1/4, 3/4, 1/8, 7/8, 3/8, 5/8, 1/8, 7/8, 3/8, 5/8, ...

Mathematica

b[1]=1; b[n_]:=b[n]=If[EvenQ[n], b[n/2]/2, 1-b[(n-1)/2]/2]; a[n_]:=Numerator[b[n]]; Array[a, 75]

Crossrefs

Cf. A053644 (denominators).

Sequence in context: A395058 A135521 A344763 * A176032 A218403 A318506

Adjacent sequences: A380440 A380441 A380442 * A380444 A380445 A380446

Keyword

nonn,easy,frac,look

Author

Stefano Spezia, Jun 21 2025

Status

approved