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

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

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

This is for a terminal assess code in the game no mans sky. The 3 choices they give are; 720, 620, 180

The next number is $840$. The $n$th term in the sequence is 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 term is the greatest fourth-power-free divisor of $n!$.

Hold on ... :)

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

After some testing I discovered that these numbers are 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 mean the next number in the sequence would be

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

Edit: Thanks to

GEdgar in the comments for helping me make pretty cool discovery about these numbers. The totals are also made up of multiplying each number up to 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 next 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 it is each term is the term before times the next counting number.

See more: Byzantine Scholars Produced Many Notable Books Especially In The Field Of A

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. Please find another price , a little bit original :) perhaps with the sum of the digits ? note also that it begins with 1 2 and ends with 120. Perhaps its an opportunity to concatenate and add zeroes. Good luck $endgroup$

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