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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#28 2013-04-15 10:13:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#30 2013-04-15 10:15:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Julianthemath's number 3

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#32 2013-04-15 10:19:20

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#34 2013-04-15 10:29:32

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#36 2013-04-15 11:19:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Julianthemath's number 3

The recurrence is not working.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#38 2013-04-15 11:28:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#40 2013-04-15 11:40:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

mathaholic
Member
From: Earth
Registered: 2012-11-29
Posts: 3,251

Re: Julianthemath's number 3

Julianthemath's discovery 5 soon!

Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#43 2013-04-15 11:51:03

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Julianthemath's number 3

Yes, I have it working now.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#45 2013-04-15 13:59:08

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#47 2013-04-15 20:45:05

mathaholic
Member
From: Earth
Registered: 2012-11-29
Posts: 3,251

Re: Julianthemath's number 3

Yes!

Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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
The knowledge of some things as a function of age is a delta function.

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#50 2013-04-15 21:59:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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