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#26 2013-04-15 10:01:27

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#27 2013-04-15 10:09:37

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

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


“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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#28 2013-04-15 10:13:04

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#29 2013-04-15 10:14:10

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

Yes. a_n's in binary.


“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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#30 2013-04-15 10:15:57

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: Julianthemath's number 3

Do you have access to m?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#31 2013-04-15 10:18:17

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

I did 30 minutes ago. Now I do not.


“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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#32 2013-04-15 10:19:20

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#33 2013-04-15 10:20:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

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


“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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#34 2013-04-15 10:29:32

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#35 2013-04-15 11:16:58

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

a_1=1.

I will look at that later.


“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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#36 2013-04-15 11:19:12

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: Julianthemath's number 3

The recurrence is not working.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#37 2013-04-15 11:21:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

What do you mean?


“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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#38 2013-04-15 11:28:04

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#39 2013-04-15 11:34:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

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


“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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#40 2013-04-15 11:40:18

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#41 2013-04-15 11:41:12

mathaholic
Member
From: Juliania
Registered: 2012-11-29
Posts: 2,849
Website

Re: Julianthemath's number 3

Julianthemath's discovery 5 soon!


"Double the fun, double the thrill, double the coolness" - Julianthewiki

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#42 2013-04-15 11:43:56

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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].


“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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#43 2013-04-15 11:51:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: Julianthemath's number 3

Yes, I have it working now.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#44 2013-04-15 12:39:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

Great! What now?

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


“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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#45 2013-04-15 13:59:08

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: Julianthemath's number 3

Here is the first 20 or so:

View Image: 2013-04-15_184040.gif

In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#46 2013-04-15 18:52:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Julianthemath's number 3

So, there is a pattern, alright!


“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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#47 2013-04-15 20:45:05

mathaholic
Member
From: Juliania
Registered: 2012-11-29
Posts: 2,849
Website

Re: Julianthemath's number 3

Yes!


"Double the fun, double the thrill, double the coolness" - Julianthewiki

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#48 2013-04-15 21:20:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#49 2013-04-15 21:55:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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?


“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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#50 2013-04-15 21:59:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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