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## #26 2013-04-16 08:01:27

bobbym

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### Re: Julianthemath's number 3

Yikes! What question are you asking? You can not expect a closed form for that recurrence.

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.

## #27 2013-04-16 08:09:37

anonimnystefy
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### Re: Julianthemath's number 3

Hm, maybe we can watch how the binary representation changes?

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

## #28 2013-04-16 08:13:04

bobbym

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### Re: Julianthemath's number 3

I am not following you. The binary representation of the output sequence?

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.

## #29 2013-04-16 08:14:10

anonimnystefy
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### Re: Julianthemath's number 3

Yes. a_n's in binary.

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

## #30 2013-04-16 08:15:57

bobbym

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### Re: Julianthemath's number 3

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.

## #31 2013-04-16 08:18:17

anonimnystefy
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### Re: Julianthemath's number 3

I did 30 minutes ago. Now I do not.

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

## #32 2013-04-16 08:19:20

bobbym

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### Re: Julianthemath's number 3

Okay, give me some time to enter the recurrence and compute some numbers.

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.

## #33 2013-04-16 08:20:21

anonimnystefy
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### Re: Julianthemath's number 3

Is there an M command for binary to decimal and decimal to binary conversion?

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

## #34 2013-04-16 08:29:32

bobbym

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### Re: Julianthemath's number 3

What are the initial conditions for the difference equation?

Go into the pull down menu for help,

Virtual Book > Mathematics and Algorithms > Numbers > Digits in Numbers

there is all the information you need.

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.

## #35 2013-04-16 09:16:58

anonimnystefy
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### Re: Julianthemath's number 3

a_1=1.

I will look at that later.

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

## #36 2013-04-16 09:19:12

bobbym

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### Re: Julianthemath's number 3

The recurrence is not working.

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.

## #37 2013-04-16 09:21:18

anonimnystefy
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### Re: Julianthemath's number 3

What do you mean?

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

## #38 2013-04-16 09:28:04

bobbym

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### Re: Julianthemath's number 3

I have probably misunderstood something so let me check each part. In post #25, does that replace the Xor as well as the binary representation ?

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.

## #39 2013-04-16 09:34:38

anonimnystefy
Real Member

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### Re: Julianthemath's number 3

It does not replace the xor. Just the binary stuff.

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

## #40 2013-04-16 09:40:18

bobbym

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### Re: Julianthemath's number 3

So this expression

is xored with a[n-1]?

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.

## #41 2013-04-16 09:41:12

mathaholic
Star Member

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### Re: Julianthemath's number 3

Julianthemath's discovery 5 soon!

246 pages on Prime Numbers Wiki (+1)

## #42 2013-04-16 09:43:56

anonimnystefy
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### Re: Julianthemath's number 3

#### bobbym wrote:

So this expression

is xored with a[n-1]?

You haven't copied it correctly.

But, yes. We xor that with a[n-1].

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

## #43 2013-04-16 09:51:03

bobbym

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### Re: Julianthemath's number 3

Yes, I have it working now.

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.

## #44 2013-04-16 10:39:54

anonimnystefy
Real Member

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### Re: Julianthemath's number 3

Great! What now?

By the way, I just read Heinlein's "And he built a crooked house".

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

## #45 2013-04-16 11:59:08

bobbym

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### Re: Julianthemath's number 3

Here is the first 20 or so:

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.

## #46 2013-04-16 16:52:57

anonimnystefy
Real Member

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### Re: Julianthemath's number 3

So, there is a pattern, alright!

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

## #47 2013-04-16 18:45:05

mathaholic
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### Re: Julianthemath's number 3

Yes!

246 pages on Prime Numbers Wiki (+1)

## #48 2013-04-16 19:20:43

bobbym

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### Re: Julianthemath's number 3

So, there is a pattern, alright!

Everything that glitters is not gold.

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.

## #49 2013-04-16 19:55:56

anonimnystefy
Real Member

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### Re: Julianthemath's number 3

That is true. I do not know how to get a general form from those.

Have you tried FindSequenceFunction on the terms?

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

## #50 2013-04-16 19:59:22

bobbym

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### Re: Julianthemath's number 3

That was the second thing I did.

In chained notation:

M = Newton -> Euler -> Fermat

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.