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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Yikes! What question are you asking? You can not expect a closed form for that recurrence.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,611

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I am not following you. The binary representation of the output sequence?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Yes. a_n's in binary.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Do you have access to m?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I did 30 minutes ago. Now I do not.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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
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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.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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a_1=1.

I will look at that later.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

The recurrence is not working.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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What do you mean?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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 ?

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**anonimnystefy****Real Member**- From: The Foundation
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It does not replace the xor. Just the binary stuff.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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So this expression

is xored with a[n-1]?

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
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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
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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: 89,150

Yes, I have it working now.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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
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Here is the first 20 or so:

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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So, there is a pattern, alright!

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**mathaholic****Member**- From: Juliania
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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
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So, there is a pattern, alright!

Everything that glitters is not gold.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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: 89,150

That was the second thing I did.

In chained notation:

M = Newton -> Euler -> Fermat

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