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

I to be playing through No Man"s Sky once I ran into a series of numbers and was inquiry 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 provide are; 720, 620, 180  The next number is \$840\$. The \$n\$th term in the sequence is the the smallest number v \$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 hatchet is the greatest fourth-power-free divisor that \$n!\$.

Hold on ... :)

Probably the answer they"re spring for, though, is \$6! = 720\$. Yet there room lots of various other justifiable answers! After some trial and error I discovered that this numbers room being multiply by their equivalent number in the sequence.

For example:

1 x 2 = 22 x 3 = 66 x 4 = 2424 x 5 = 120Which would mean 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 do 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 following number is 720.

The sequence is the factorials:

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

6! = 720.

(Another method to think of that is each term is the term prior to times the next counting number.

See more: How Many Beers To Get Drunk ? Why You Can'T Get Drunk On 0

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 however done. You re welcome find another answer , a tiny bit original :) possibly with the amount of the digits ? note likewise that it begins with 1 2 and also ends through 120. Maybe its an opportunity to concatenate and include zeroes. An excellent luck \$endgroup\$

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