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You are watching: 1-2-6-24 pattern
I to be playing through No Man"s Sky when I ran into a collection of numbers and also was request what the following number would certainly be.
$$1, 2, 6, 24, 120$$
This is for a terminal assess code in the game no man sky. The 3 options they give are; 720, 620, 180
The following number is $840$. The $n$th hatchet in the succession is the the smallest number v $2^n$ divisors.
Er ... The following number is $6$. The $n$th hatchet is the the very least factorial many of $n$.
No ... Wait ... It"s $45$. The $n$th term is the biggest fourth-power-free divisor that $n!$.
Hold on ... :)
Probably the prize they"re spring for, though, is $6! = 720$. Yet there space lots of other justifiable answers!
After some experimentation I found that this numbers are being multiplied by their corresponding 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 certainly be
120 x 6 = 720and for this reason on and so forth.
Edit: many thanks to
GEdgar in the comments because that helping me do pretty cool discovery around these numbers. The totals are also made up of multiplying each number up to 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 following number is 720.
The succession is the factorials:
1 2 6 24 120 = 1! 2! 3! 4! 5!
6! = 720.
(Another means to think of that is each term is the term prior to 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 however done. Please find one more answer , a tiny bit original :) possibly with the amount of the number ? note additionally that it begins with 1 2 and ends through 120. Maybe its an chance to concatenate and add zeroes. Good luck $endgroup$
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