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#76 2013-04-18 00:35:52

bobbym

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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#77 2013-04-18 00:44:51

anonimnystefy
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Re: Julianthemath's number 3

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#78 2013-04-18 00:51:43

bobbym

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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#79 2013-04-18 00:53:59

anonimnystefy
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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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#80 2013-04-18 00:59:26

bobbym

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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#81 2013-04-18 01:11:39

anonimnystefy
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Re: Julianthemath's number 3

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#82 2013-04-18 01:13:50

bobbym

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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#83 2013-04-18 01:54:36

anonimnystefy
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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 (2013-04-18 02:41:07)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#84 2013-04-18 01:56:00

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#85 2013-04-18 01:57:42

anonimnystefy
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Re: Julianthemath's number 3

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#86 2013-04-18 01:59:41

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#87 2013-04-18 02:01:24

anonimnystefy
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Re: Julianthemath's number 3

I think you will get the same solution.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#88 2013-04-18 02:04:20

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#89 2013-04-18 02:13:04

anonimnystefy
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Re: Julianthemath's number 3

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#90 2013-04-18 02:16:56

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#91 2013-04-18 02:26:28

anonimnystefy
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Re: Julianthemath's number 3

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#92 2013-04-18 02:28:04

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#93 2013-04-18 02:29:53

anonimnystefy
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Re: Julianthemath's number 3

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#94 2013-04-18 02:33:02

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#95 2013-04-18 02:41:46

anonimnystefy
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Re: Julianthemath's number 3

How?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#96 2013-04-18 02:44:19

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#97 2013-04-18 02:47:50

anonimnystefy
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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?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#98 2013-04-18 02:50:51

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#99 2013-04-18 02:56:39

anonimnystefy
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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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#100 2013-04-18 03:04:20

bobbym

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.