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

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

This is because that a terminal assess password in the video game no man sky. The 3 selections they offer are; 720, 620, 180

The following number is $840$. The $n$th ax in the succession is the the smallest number with $2^n$ divisors.

Er ... The next number is $6$. The $n$th term is the least factorial multiple of $n$.

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

Hold ~ above ... :)

Probably the prize they"re looking for, though, is $6! = 720$. Yet there are *lots* of various other justifiable answers!

After some experimentation I discovered that these numbers room 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 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 additionally made increase of multiplying every number approximately that present 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 means to think of the is every term is the term prior to times the next counting number.

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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 yet done. You re welcome find another answer , a small bit original :) perhaps with the amount of the number ? note additionally that it begins with 1 2 and ends with 120. Probably its an opportunity to concatenate and include zeroes. An excellent luck $\endgroup$

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