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  •  » Prime sum of three term arithmetic progression?

#1 2013-04-30 22:28:35

anonimnystefy
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Prime sum of three term arithmetic progression?

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:

Code:

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 (2013-05-01 01:49:56)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#2 2013-05-01 05:08:19

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-05-01 05:42:49

anonimnystefy
Real Member

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Re: Prime sum of three term arithmetic progression?

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#4 2013-05-01 06:54:31

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2013-05-01 07:01:27

anonimnystefy
Real Member

Offline

Re: Prime sum of three term arithmetic progression?

Csbfc?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#6 2013-05-01 10:06:26

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

Nope, CSBFC.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2013-05-01 16:43:19

anonimnystefy
Real Member

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Re: Prime sum of three term arithmetic progression?

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#8 2013-05-01 18:44:18

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

CommonSense, Brute Force and the Computer.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#9 2013-05-02 04:27:09

anonimnystefy
Real Member

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Re: Prime sum of three term arithmetic progression?

Sound like a good name for a book.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#10 2013-05-02 04:29:00

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

Not a book, a dynamite article though.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11 2013-05-02 04:37:11

anonimnystefy
Real Member

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Re: Prime sum of three term arithmetic progression?

Sure. Why not!

By the way, I like your new avatar.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#12 2013-05-02 04:38:48

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#13 2013-05-02 04:44:04

anonimnystefy
Real Member

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Re: Prime sum of three term arithmetic progression?

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?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#14 2013-05-02 04:47:49

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#15 2013-05-02 04:53:31

anonimnystefy
Real Member

Offline

Re: Prime sum of three term arithmetic progression?

Yes, I did.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#16 2013-05-02 04:55:51

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#17 2013-05-02 04:57:33

anonimnystefy
Real Member

Offline

Re: Prime sum of three term arithmetic progression?

We established exactly the opposite.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#18 2013-05-02 04:59:18

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#19 2013-05-03 18:59:07

pgoh63
Novice

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Re: Prime sum of three term arithmetic progression?

I need help to find the nth for this sequence :

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

Pls help.

#20 2013-05-03 19:13:00

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#21 2013-05-03 19:15:46

anonimnystefy
Real Member

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Re: Prime sum of three term arithmetic progression?

Hi pgoh63

I am getting 3/16 as the next term.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#22 2013-05-06 11:36:45

pgoh63
Novice

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Re: Prime sum of three term arithmetic progression?

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.

#23 2013-05-09 05:04:23

anonimnystefy
Real Member

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Re: Prime sum of three term arithmetic progression?

Hi pgoh63

Have you seen my answer?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#24 2013-05-09 05:11:30

bobbym
Administrator

Online

Re: Prime sum of three term arithmetic progression?

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


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#25 2013-05-09 05:15:24

anonimnystefy
Real Member

Offline

Re: Prime sum of three term arithmetic progression?

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.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
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