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July 10th, 2016, 06:01 AM  #1 
Senior Member Joined: Mar 2015 From: England Posts: 162 Thanks: 4  How do I find the Fourier series of a pattern?
[IMG][/IMG] At last I can upload pictures! So as you may well have guessed, this is following on from my attempt at finding a pattern to prime numbers. The graph above goes from 1 to 1,000. The graph below is 1 to 30 with (x,y) coordinates. Each graphs x and y coordinates have no fractional numbers. I've been trying to learn how to do this for a week and I got pretty close. For the x axis there are natural numbers going from 1 to infinity. and for the y axis I have J up to infinity going up and J to infinity going down. So x is cos and y is I sin, f(x) is isin. it's all done in radians. They can all be polar coordinated or Cartesian coordinates. I just can't wrap my head around the infinite fourier series. 
July 10th, 2016, 07:24 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 476 Thanks: 119 
The graph has to be periodic to find a fourier series. The interval between primes is not periodic so your attempt will fail. Sorry. 
July 10th, 2016, 09:43 AM  #3 
Senior Member Joined: Mar 2015 From: England Posts: 162 Thanks: 4 
These are not prime numbers, these are the numbers that when divided by the Pronic numbers (CoPrime) make a differential that when added to the previously added differentials make a number which when multiplied by its natural number makes the next prime. Mmmm this is good to know, I will continue looking for the function by some other means. 
July 10th, 2016, 10:34 AM  #4 
Senior Member Joined: Mar 2015 From: England Posts: 162 Thanks: 4 
Ah I see, so would the graph below be considered a linear combination?

July 10th, 2016, 11:19 AM  #5 
Senior Member Joined: Jun 2015 From: England Posts: 476 Thanks: 119 
A linear (or even non linear) combination of what? As I said the interval between primes is not periodic eg 1  2, INTERVAL = 1 eg 2  3, INTERVAL = 1 But 3  5 Interval = 2 People have been searching for centuries for a function to list primes and I'm not sure if it has even been proved impossible. Perhaps someone more into number theory might help here with comments? Meanwhile the book on number theory by G H Hardy is a good start https://www.amazon.co.uk/Introductio.../dp/0199219869 
July 10th, 2016, 11:49 AM  #6 
Senior Member Joined: Mar 2015 From: England Posts: 162 Thanks: 4 
Thankyou. I admit I must be confusing to respond to because I don't have the names quite right. I might just try to go solo now.

July 10th, 2016, 01:12 PM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,490 Thanks: 557 Math Focus: Wibbly wobbly timeywimey stuff. 
I'm not sure what all you are trying to do with the Fourier transform, but you could take a number N points on your graph and approximate them by a Fourier transform over that interval. The approximation may/may not be good but you see what would happen. Dan 
July 11th, 2016, 09:59 AM  #8 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,250 Thanks: 560 
A function, defined over a finite interval, as is the case here, with x from 0 to 30, does NOT have to be periodic you think of the function as repeating with that period.

July 11th, 2016, 12:58 PM  #9 
Senior Member Joined: Jun 2015 From: England Posts: 476 Thanks: 119 
Hello topsquark: As I understand it, the OP requested a fourier series, not transform, so he could predict further prime numbers. Country boy, that could only work if the ends match. Do they and do they then generate prime numbers? 
July 11th, 2016, 02:28 PM  #10 
Senior Member Joined: Mar 2015 From: England Posts: 162 Thanks: 4 
Hello all i'm looking into prime number and quantum mechanics connections right now sommething called eivongor problems? I'm just trying tofind anything that may provide a pattern for these numbers which when divided by pronic makes a differential which when added to existing differentials makes a linear combination which then timsed by natural makes prime. All ideas are welcome.


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