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Extension to Sharky Kesa's problem

If you haven't seen this problem yet, do try it out. Spoilers follow.

I would like to propose an extension: is it possible to improve the bound \(O(n!^3)\)?

An idea I had is start with a primorial cubed, multiply by 8 each step, until the next primorial cubed is needed. Of course, this would allow arbitrarily large subsequences of geometric sequences, so we will not allow increments of 8, ie \(\dfrac{t_{n+1}}{t_n}\) is strictly monotonically increasing.

Note by Jake Lai
1 year, 7 months ago

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  Easy Math Editor

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**bold** or __bold__ bold

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  • bulleted
  • list

1. numbered
2. list

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paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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