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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Here is a problem I found on brilliant.org

Consider all 3-term geometric sequences with first term 1 and with common ratio the square of an integer between 1 and 1000 (inclusive). How many of these 1000 geometric sequences have the property that the sum of the 3 terms is prime?

I wrote this M code to do it:

`Select[Table[1+q^2+q^4,{q,1,Floor[Sqrt[1000]]}],PrimeQ[#]&]//Length`

but I am suspecting there is a better way to do it. Does anyone know of a better and/or shorter way to do it?

*Last edited by anonimnystefy (2013-04-30 03:49:56)*

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: 86,636

Hi;

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

I haven't noticed that at all. I was focused on finding an M only solution.

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: 86,636

Hi;

The M solution is fine. There might be a faster way but in this case the CSBFC principle applies.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Csbfc?

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: 86,636

Nope, CSBFC.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

That is what I wrote, but the forum tirns it lower case automatically. What does that acronym mean?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

CommonSense, Brute Force and the Computer.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Sound like a good name for a book.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

Not a book, a dynamite article though.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Sure. Why not!

By the way, I like your new avatar.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

It already happened and I was the only person who read it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

The only mention of that article on the Internet is on this forum by you. I am guessing you are the guy who never got it published?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

Hmmmm, it appears you did not read everything I said about that article.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Yes, I did.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

bobbym wrote:

A brilliant guy I knew wrote an article for a famous computer journal called

"Common Sense, Brute Force and the Computer." It did not get published and it

was a really great article.

We have already established in the other thread that though I may look brilliant and smell brilliant, I am not brilliant,

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

We established exactly the opposite.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

I am afraid that it is difficult to establish assertions that are untrue.

The author was brilliant, I am not, therefore I am not the author.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**pgoh63****Member**- Registered: 2013-05-02
- Posts: 2

I need help to find the nth for this sequence :

1, 1, 3/4, 1/2, 5/16

Pls help.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

Hi pgoh63;

Where does the sequences come from? There are a lot of possible fits for it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi pgoh63

I am getting 3/16 as the next term.

Here lies the reader who will never open this book. He is forever dead.

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**pgoh63****Member**- Registered: 2013-05-02
- Posts: 2

I got this from my girl's school homework. Not sure if there is any typo errors....I also suspect the fifth term might be wrong. Will check with the school teacher.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi pgoh63

Have you seen my answer?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

Is it the same answer if the fifth term is wrong?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Maybe and maybe not. Until he posts the correct fifth term we cannot know.

But it seems he got that idea because you said there were many possible fits.

Here lies the reader who will never open this book. He is forever dead.

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