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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

Nope, CSBFC.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

CommonSense, Brute Force and the Computer.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Sound like a good name for a book.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

Not a book, a dynamite article though.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Sure. Why not!

By the way, I like your new avatar.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

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?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Yes, I did.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

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,

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

We established exactly the opposite.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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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: 102,390

Hi pgoh63;

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Hi pgoh63

I am getting 3/16 as the next term.

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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**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: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Hi pgoh63

Have you seen my answer?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,390

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

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.

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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