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#76 2013-04-17 02:35:52

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

That is very good, you kept the dominant terms.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#77 2013-04-17 02:44:51

anonimnystefy
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Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

Exactly. They seem to do the job good enough. I will try getting the closed form analitically today.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#78 2013-04-17 02:51:43

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

Uh wait. That is the analytical answer up there. So you will looking for a shorter one?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#79 2013-04-17 02:53:59

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

You didn't get it by analityc methods. You used M's FindSequenceFunction command. I want to see if I can get the answer analitically.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#80 2013-04-17 02:59:26

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

All you provided me was with your original algorithm. I had to use the sequence. And why not just try induction and prove the a_n is correct?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#81 2013-04-17 03:11:39

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

Do you think there is a nicer reccurence for the sequence?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#82 2013-04-17 03:13:50

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

Maybe. The weirdest thing is that sequences can have more than one difference equation.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#83 2013-04-17 03:54:36

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

I have the difference equation. It's a[n+4]-4a[n+2]-a[n]+4a[n-2]=0. Don't ask how I got it!

Last edited by anonimnystefy (2013-04-17 04:41:07)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#84 2013-04-17 03:56:00

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

I am going to ask just that.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#85 2013-04-17 03:57:42

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

It is a bit tough to explain. I played a little bit of spot-the-pattern...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#86 2013-04-17 03:59:41

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

The solution to that will probably be longer than the other one.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#87 2013-04-17 04:01:24

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

I think you will get the same solution.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#88 2013-04-17 04:04:20

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

Possibly, or the trigonometric terms will be replaced by (-1)^n or something like that.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#89 2013-04-17 04:13:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

The trigonometric terms will be replaced by i^n and (-i)^n.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#90 2013-04-17 04:16:56

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

Yes, that is possible too but I would not exactly call that simpler.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#91 2013-04-17 04:26:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

True. But the reduced form looks really nice, though!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#92 2013-04-17 04:28:04

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

It is an asymptotic form yes? It is supposed to be shorter and easier to compute.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#93 2013-04-17 04:29:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

Yes. It looks much much prettier than the nasty exact one.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#94 2013-04-17 04:33:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

But you possibly missed the forest for the trees.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#95 2013-04-17 04:41:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

How?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#96 2013-04-17 04:44:19

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

It appears there might be a pattern worth investigating that is much simpler. It may not hold but it is worth a look. You have to get out of the box axiomatic math puts you in. It is small, dark and has little air.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#97 2013-04-17 04:47:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

Which pattern? In the binary representation? That is the one I used to get the difference equation.

Hm, could you do asymptotic_a[n]-a[n] for me?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#98 2013-04-17 04:50:51

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

One question at a time can be investigated well. This one is more important.

Which pattern? In the binary representation?

No, not that one. Look below, is there anything cooking?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#99 2013-04-17 04:56:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Julianthemath's number 3

Well, they approach 1. That is why my formula is an asymptotic one. I also notice that every fourth term repeats two terms later. I do not notice anything else.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#100 2013-04-17 05:04:20

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Julianthemath's number 3

Yes, the differences between the asymptotic form and the actual answer follow a pattern.

1,3, then 1,1,1,3...

This suggests 2 recurrences and just adding the appropriate constant. Now you would have a short exact answer.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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