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You are watching: 1,2,6,24,120
I to be playing with No Man"s Sky once I ran right into a collection of numbers and was asked what the next number would certainly be.
$$1, 2, 6, 24, 120$$
This is for a terminal assess password in the video game no man sky. The 3 options they offer are; 720, 620, 180
The following number is $840$. The $n$th ax in the sequence is the the smallest number through $2^n$ divisors.
Er ... The following number is $6$. The $n$th ax is the the very least factorial many of $n$.
No ... Wait ... It"s $45$. The $n$th term is the best fourth-power-free divisor of $n!$.
Hold on ... :)
Probably the price they"re looking for, though, is $6! = 720$. But there are lots of other justifiable answers!
After some trial and error I found that this 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 typical 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 also made increase of multiplying each number approximately 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 way to think of that is each term is the term before times the next counting number.
See more: Which Artist Made The Concept Of Collage Into A Form Of Art In 1912?
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 one more answer , a little bit initial :) maybe with the amount of the number ? note also that it starts with 1 2 and ends through 120. Possibly its an possibility to concatenate and add zeroes. An excellent luck $endgroup$
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