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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Yes. a_n's in binary.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

Do you have access to m?

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

a_1=1.

I will look at that later.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

The recurrence is not working.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

What do you mean?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

So this expression

is xored with a[n-1]?

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

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,895
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Julianthemath's discovery 5 soon!

"What is the square root of 2? 1.4141592653589793238" Seriously, I thought it was that. Too round?

3.141592653589793238...

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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].

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

Yes, I have it working now.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Great! What now?

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

Here is the first 20 or so:

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

So, there is a pattern, alright!

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
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Yes!

"What is the square root of 2? 1.4141592653589793238" Seriously, I thought it was that. Too round?

3.141592653589793238...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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

Have you tried FindSequenceFunction on the terms?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

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.**

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