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You are watching: 1-2-6-24-120
I was playing with No Man"s Sky when 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 mans sky. The 3 options they offer are; 720, 620, 180
The next number is $840$. The $n$th term in the sequence is the the smallest number through $2^n$ divisors.
Er ... The next number is $6$. The $n$th hatchet is the least factorial lot of of $n$.
No ... Wait ... It"s $45$. The $n$th ax is the biggest fourth-power-free divisor that $n!$.
Hold ~ above ... :)
Probably the answer they"re spring for, though, is $6! = 720$. Yet there space lots of other justifiable answers!
After some experimentation I found that this numbers room being multiply by their equivalent 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 around these numbers. The totals are additionally made up of multiplying every number approximately that current 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 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 the is every term is the term before times the next 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.
$egingroup$ it's yet done. You re welcome find another answer , a small bit original :) perhaps with the sum of the number ? note likewise that it starts with 1 2 and ends with 120. Maybe its an possibility to concatenate and include zeroes. Great luck $endgroup$
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