×

# 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

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 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} $$\boxed{123}$$