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

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

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

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

The next number is \$840\$. The \$n\$th hatchet 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 lot of of \$n\$.

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

Hold on ... :)

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

After some experimentation I uncovered that this numbers room 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 average the following number in the sequence would be

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

Edit: thanks to
GEdgar in the comments because that helping me make pretty cool discovery around these numbers. The totals are also made up of multiplying each number as much as 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 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 every term is the term prior to times the following counting number.

See more: What Is The Electron Configuration For Tungsten (W) Compared To Chromium (Cr)

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 an additional answer , a small bit original :) maybe with the sum of the digits ? note also that it begins with 1 2 and ends through 120. Probably its an chance to concatenate and include zeroes. An excellent luck \$endgroup\$

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

Is there any type of discernible pattern because that the number perform \$frac73, frac54, 1, frac89, ...\$
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