Want to enhance this question? include details and clarify the difficulty by editing this post.

Closed 5 year ago.

You are watching: 1,2,6,24,120

I to be playing with No Man"s Sky once I ran right into a collection of numbers and was asked what the next number would certainly be.

\$\$1, 2, 6, 24, 120\$\$

This is for a terminal assess password in the video game no man sky. The 3 options they offer are; 720, 620, 180  The following number is \$840\$. The \$n\$th ax in the sequence is the the smallest number through \$2^n\$ divisors.

Er ... The following number is \$6\$. The \$n\$th ax is the the very least factorial many of \$n\$.

No ... Wait ... It"s \$45\$. The \$n\$th term is the best fourth-power-free divisor of \$n!\$.

Hold on ... :)

Probably the price they"re looking for, though, is \$6! = 720\$. But there are lots of other justifiable answers! After some trial and error I found that this numbers space being multiply by their matching number in the sequence.

For example:

1 x 2 = 22 x 3 = 66 x 4 = 2424 x 5 = 120Which would typical the next number in the sequence would be

120 x 6 = 720and for this reason on and also so forth.

Edit: thanks to
GEdgar in the comments because that helping me make pretty cool discovery about these numbers. The totals are also made increase of multiplying each number approximately that existing count.

For Example:

2! = 2 x 1 = 23! = 3 x 2 x 1 = 64! = 4 x 3 x 2 x 1 = 245! = 5 x 4 x 3 x 2 x 1 = 1206! = 6 x 5 x 4 x 3 x 2 x 1 = 720 The following number is 720.

The sequence is the factorials:

1 2 6 24 120 = 1! 2! 3! 4! 5!

6! = 720.

(Another way to think of that is each term is the term before times the next counting number.

See more: Which Artist Made The Concept Of Collage Into A Form Of Art In 1912?

T0 = 1; T1 = T0 * 2 = 2; T2 = T1 * 3 = 6; T3 = T2 * 4 = 24; T4 = T3 * 5 = 120; T5 = T4 * 6 = 720. \$egingroup\$ it's yet done. You re welcome find one more answer , a little bit initial :) maybe with the amount of the number ? note also that it starts with 1 2 and ends through 120. Possibly its an possibility to concatenate and add zeroes. An excellent luck \$endgroup\$

## Not the price you're spring for? Browse various other questions tagged sequences-and-series or asking your own question.

Is there any kind of discernible pattern for the number perform \$frac73, frac54, 1, frac89, ...\$
site design / logo © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.11.40730

her privacy

By clicking “Accept all cookies”, friend agree ridge Exchange deserve to store cookies on your an equipment and disclose info in accordance through our Cookie Policy.