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Powers of integers and factorials 
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#1
Mar1311, 10:16 PM

P: 4

I would like some direction on studying powers of integers and if they are in any way related to factorials. I was studying the sequence of cubics 1, 8, 27, 64, 125 and so. After a certain number of rounds of a basic rule I choose to apply to this sequence, I arrived at a new sequence where one particular integer (not 0 nor 1) was repeated. I tried a sequence of integers raised to fourth power and found that my process brought about similar results. Depending on the exponent ( natural number ) used on the integers that I write out, I can now predict how many rounds it will take to get to the repeated integer and also predict that the repeated integer is a certain factorial. I am not referring to 0! nor 1! Does this discovery for me seem important or useful to any branch of math? I am new at asking questions here; I enjoy patterns with numbers and am trying to write conjectures or maybe a theorem or two from my discoveries. thanks for the help .



#2
Mar1411, 06:11 AM

P: 828

You are going to have to tell us what rule you used. 


#3
Mar1411, 09:34 AM

P: 153

For whatever its worth, without any reference to factorials, the digital root of n^3 is 1, 8, 9 repeating, while the digital root of the sum of cubes (Triangular Numbers Squared) is 1,9,9 repeating. As opposed, for instance, to the digital root of n^2, which is 1,4,9,7,7,9,4,1,9 repeating.
Curious what your "rule" is. 


#4
Mar1411, 11:45 AM

P: 4

Powers of integers and factorials
Why would the rule be important in order to give me some direction? It is a simple rule applied to all terms of the sequence. Is there a known relationship between integers raised to a specific power and a factorial?



#5
Mar1411, 11:34 PM

P: 153

Might the answer to that question not depend on what base was our mutual reference point? Let me be the first to assure you: whatever you are or are not "on to" is probably quite trivial, even if correct. 


#6
Mar1511, 10:13 AM

P: 894




#7
Mar1511, 11:30 AM

P: 4

Thanks for that help. I am in a bit of rush right now but I will look into that more. I am not really working with a series, just the sequence of integers. For example do you know how to relate 1^3, 2^3, 3^3, 4^3 and so on to 3! ?



#8
Mar1511, 12:14 PM

P: 894




#9
Mar1511, 04:12 PM

P: 688



#10
Mar1511, 09:23 PM

P: 4

Thanks very much Dodo. That is very close to what I was looking for. I will study what K. W. has to offer!



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