Want to boost this question? add details and also clarify the trouble by editing this post.

Closed 5 year ago.

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

I to be playing v No Man"s Sky when I ran right into a collection of numbers and was request what the following number would be.

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

This is because that a terminal assess code in the game no mans sky. The 3 choices they provide are; 720, 620, 180  The next number is $840$. The $n$th ax in the succession is the the smallest number v $2^n$ divisors.

Er ... The next number is $6$. The $n$th hatchet is the least factorial many of $n$.

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

Hold top top ... :)

Probably the price they"re looking for, though, is $6! = 720$. But there room lots of other justifiable answers! After some experimentation I discovered that these numbers space being multiplied by their corresponding number in the sequence.

For example:

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

120 x 6 = 720and therefore on and so forth.

Edit: many thanks to
GEdgar in the comments for helping me do pretty cool discovery around these numbers. The totals are also made increase of multiplying every number as much as that current 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 succession is the factorials:

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

6! = 720.

(Another means to think of the is every term is the term prior to times the following counting number.

See more: What Is 2/ 8 Divided By 1/2 0, Fraction Calculator: 7/8 Divided By 1/20

T0 = 1; T1 = T0 * 2 = 2; T2 = T1 * 3 = 6; T3 = T2 * 4 = 24; T4 = T3 * 5 = 120; T5 = T4 * 6 = 720. $\begingroup$ it's however done. You re welcome find one more answer , a tiny bit initial :) maybe with the amount of the number ? note additionally that it begins with 1 2 and ends through 120. Perhaps its an chance to concatenate and include zeroes. Great luck $\endgroup$

## Not the prize you're looking for? Browse various other questions tagged sequences-and-series or questioning your very own question.

Is there any discernible pattern for the number list $\frac73, \frac54, 1, \frac89, ...$
site design / logo © 2021 ridge Exchange Inc; user contributions licensed under cc by-sa. Rev2021.9.30.40353