benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let N be the set of positive integers, and let f:N→N be a function satisfying f(1)=1 and for n∈N,f(2n)=2f(n) and f(2n+1)=2f(n)−1. Determine the sum of all positive integer solution…

Problem

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

problem

Let N\mathbb{N} be the set of positive integers, and let f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} be a function satisfying f(1)=1f(1)=1 and for n∈N,f(2n)=2f(n)n \in \mathbb{N}, f(2 n)=2 f(n) and f(2n+1)=2f(n)−1f(2 n+1)=2 f(n)-1. Determine the sum of all positive integer solutions to f(x)=19f(x)=19 that do not exceed 2019.
Plain-text mathematical notation (without MathML)
Let N be the set of positive integers, and let f:N→N be a function satisfying f(1)=1 and for n∈N,f(2n)=2f(n) and f(2n+1)=2f(n)−1. Determine the sum of all positive integer solutions to f(x)=19 that do not exceed 2019.
Original LaTeX notation
Let $\mathbb{N}$ be the set of positive integers, and let $f: \mathbb{N} \rightarrow \mathbb{N}$ be a function satisfying $f(1)=1$ and for $n \in \mathbb{N}, f(2 n)=2 f(n)$ and $f(2 n+1)=2 f(n)-1$. Determine the sum of all positive integer solutions to $f(x)=19$ that do not exceed 2019.

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
96840a8f-c434-55fd-9626-06a2d090805f
task_key
test--96840a8f-c434-55fd-9626-06a2d090805f
task_revision_id
1
config / split
/ test

Official source

initial import