The sequence is
$1, 4, 16, 27, 256, 3125, 46656, 65536, 823543, 16777216, 387420489, 10000000000, 285311670611, 7625597484987, 8916100448256$
Can you figure out the pattern to this sequence of numbers?
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1$\begingroup$ Just to be sure, 16 is really in this sequence? $\endgroup$– Fleury26Mar 21, 2018 at 18:52
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$\begingroup$ Yes 16 really is in this sequence. $\endgroup$– Anders GustafsonMar 21, 2018 at 18:53
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1$\begingroup$ It's a very interesting sequence, and the math behind it is fascinating, but we are somewhat picky about number sequence puzzles on this site: a puzzle whose solution can be found in the bible is not going to fare all that well. There are a couple of other hints on creating good (and bad) number sequence puzzles in the tag wiki and the linked meta question. So please do keep posting, and welcome to PSE! $\endgroup$– BassMar 21, 2018 at 20:08
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2 Answers
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A quick search on OEIS give:
The Hyper-4 powers also known as Tetration
Basically:
This is a sorted list of $a^a$, $b^{b^b}$, $c^{c^{c^c}}$ and so on... where $a,b,c,...$ are Natural numbers greater than 2 (1 is the offset in this case, 1^(any number) gives 1 )
So, the next term is: 13**13 = 302875106592253
answered Mar 21, 2018 at 18:56
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$\begingroup$ @thecoder16 I "extrapolated" that bit :P $\endgroup$ Mar 21, 2018 at 20:15
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Besides 16, the sequence is
$n^n$. $1^1=1$, $2^2=4$, $3^3=27$, etc.
