benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Does there exist a sequence F(1),F(2),F(3),… of non-negative integers that simultaneously satisfies the following three conditions? [b](a)[/b] Each of the integers 0,1,2,… occurs i…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Does there exist a sequence F(1),F(2),F(3),… F(1), F(2), F(3), \ldots of non-negative integers that simultaneously satisfies the following three conditions? [b](a)[/b] Each of the integers 0,1,2,… 0, 1, 2, \ldots occurs in the sequence. [b](b)[/b] Each positive integer occurs in the sequence infinitely often. [b](c)[/b] For any n≥2, n \geq 2, \[ F(F(n^{163})) \equal{} F(F(n)) \plus{} F(F(361)). \]
Plain-text mathematical notation (without MathML)
Does there exist a sequence F(1),F(2),F(3),… of non-negative integers that simultaneously satisfies the following three conditions?

[b](a)[/b] Each of the integers 0,1,2,… occurs in the sequence.
[b](b)[/b] Each positive integer occurs in the sequence infinitely often.
[b](c)[/b] For any n≥2,
\[ F(F(n^{163})) \equal{} F(F(n)) \plus{} F(F(361)).
\]
Original LaTeX notation
Does there exist a sequence $ F(1), F(2), F(3), \ldots$ of non-negative integers that simultaneously satisfies the following three conditions?

[b](a)[/b] Each of the integers $ 0, 1, 2, \ldots$ occurs in the sequence.
[b](b)[/b] Each positive integer occurs in the sequence infinitely often.
[b](c)[/b] For any $ n \geq 2,$
\[ F(F(n^{163})) \equal{} F(F(n)) \plus{} F(F(361)).
\]

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
4ef9e69f-26dd-5c49-ba9e-10a764cd791d
task_key
test--4ef9e69f-26dd-5c49-ba9e-10a764cd791d
task_revision_id
1
config / split
/ test

Official source

initial import