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You are watching: 1 2 6 24 120 pattern
I to be playing v No Man"s Sky when I ran right into a series of numbers and was inquiry what the following number would certainly be.
$$1, 2, 6, 24, 120$$
This is for a terminal assess password in the game no mans sky. The 3 selections they offer are; 720, 620, 180
The next number is $840$. The $n$th term in the sequence is the smallest number through $2^n$ divisors.
Er ... The next number is $6$. The $n$th term is the least factorial many of $n$.
No ... Wait ... It"s $45$. The $n$th hatchet is the best fourth-power-free divisor that $n!$.
Hold ~ above ... :)
Probably the answer they"re looking for, though, is $6! = 720$. But there room lots of other justifiable answers!
After some experimentation I discovered that these numbers space being multiply by their matching number in the sequence.
1 x 2 = 22 x 3 = 66 x 4 = 2424 x 5 = 120Which would average the next number in the sequence would certainly be
120 x 6 = 720and for this reason on and also so forth.
Edit: thanks to
GEdgar in the comments for helping me do pretty cool discovery about these numbers. The totals are additionally made up of multiplying each number as much as that existing count.
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 following 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 however done. You re welcome find one more answer , a little bit initial :) perhaps with the sum of the digits ? note additionally that it starts with 1 2 and also ends through 120. Maybe its an chance to concatenate and add zeroes. Good luck $\endgroup$
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