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

I to be playing with No Man"s Sky as soon as I ran into a series of numbers and was request what the following number would certainly be.

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

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

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

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

Hold on ... :)

Probably the answer they"re looking for, though, is $6! = 720$. However there are lots of other justifiable answers! After some experimentation I found that this numbers space being multiplied by their equivalent number in the sequence.

For example:

1 x 2 = 22 x 3 = 66 x 4 = 2424 x 5 = 120Which would median the following number in the sequence would certainly 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 about these numbers. The totals are likewise made up of multiplying every number approximately 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 way to think of it is every term is the term prior to times the next counting number.

See more: A Current Carrying Wire Is Wrapped Around Cardboard Tube As Shown Below.

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. Please find another answer , a little bit original :) maybe with the sum of the number ? note likewise that it begins with 1 2 and also ends through 120. Perhaps its an possibility to concatenate and include zeroes. An excellent luck $\endgroup$

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