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Omni-MATH / Whether there are integers a₁, a₂, ⋯, that are different from each other, satisfying: (1) For forall kinmathbb N_+, a_(k²)>0 and a_(k²+k)<0; (2) For forall ninmathbb N_+, …

Problem

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problem

Whether there are integers a1a_1, a2a_2, ⋯\cdots, that are different from each other, satisfying: (1) For $\forall k\in\mathbb N_+$, ak2>0a_{k^2}>0 and ak2+k<0a_{k^2+k}<0; (2) For $\forall n\in\mathbb N_+$, |an+1−an|≤2023n\left| a_{n+1}-a_n\right|\leqslant 2023\sqrt n?
Plain-text mathematical notation (without MathML)
Whether there are integers a₁, a₂, ⋯, that are different from each other, satisfying:
(1) For $\forall k\in\mathbb N_+$, a_(k²)>0 and a_(k²+k)<0;
(2) For $\forall n\in\mathbb N_+$, |a_(n+1)−a_(n)|≤2023√(n)?
Original LaTeX notation
Whether there are integers $a_1$, $a_2$, $\cdots$, that are different from each other, satisfying:
(1) For $\forall k\in\mathbb N_+$, $a_{k^2}>0$ and $a_{k^2+k}<0$;
(2) For $\forall n\in\mathbb N_+$, $\left| a_{n+1}-a_n\right|\leqslant 2023\sqrt n$?

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Source and history

task_id
2b2622c5-7dbc-59f1-b996-935261f253d9
task_key
test--2b2622c5-7dbc-59f1-b996-935261f253d9
task_revision_id
1
config / split
/ test

Official source

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