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Corey's Math Problem

Author

Topic

Seventhnight
Master Smack Fu Yak Hacker

2878 Posts

Posted - 2004-07-16 : 11:14:08

Solve anyway you would like (I would enjoy seeing a SQL version though):

On the topic of primes -

p(1) = 1
p(2) = 2
p(3) = 3
p(4) = 5
p(9594) = ???

Good Luck!!

Corey

jhermiz

3564 Posts

Posted - 2004-07-16 : 11:19:48

Looking for the 9594th prime ?

Jon
www.web-impulse.com

Seventhnight
Master Smack Fu Yak Hacker

2878 Posts

Posted - 2004-07-16 : 11:20:55

Yep. Well, I'm not... you are

!

Corey

jhermiz

3564 Posts

Posted - 2004-07-16 : 11:24:12

p(n) = 1 + (sum from j=3 to n) ( (j-2)! - j[(j-2)!/j] )

Do you want a C++ solution ?
Wait till I get home :)...I love this type of stuff :)

Jon
www.web-impulse.com

jhermiz

3564 Posts

Posted - 2004-07-16 : 11:25:23

O btw didnt Seive have an algorithm for this?
Will research though

Jon
www.web-impulse.com

Seventhnight
Master Smack Fu Yak Hacker

2878 Posts

Posted - 2004-07-16 : 11:30:02

Whats Seive??

btw - I'm a math major at clemson, so I also love this stuff

Corey

jhermiz

3564 Posts

Posted - 2004-07-16 : 11:34:57

Here...
Solution is pretty easy with this:

http://www.nist.gov/dads/HTML/sieve.html

Jon
www.web-impulse.com

jhermiz

3564 Posts

Posted - 2004-07-17 : 23:57:40

Sorry I'm late corey...been working long hours.

Here's a nice solution for your problem in C :)

http://www.thecenturoncompany.com/jhermiz/blog/nthprime.txt

Got any more ?

Jon
www.web-impulse.com

Can you dig it: http://www.thecenturoncompany.com/jhermiz/blog/

kselvia
Aged Yak Warrior

526 Posts

Posted - 2004-07-18 : 01:04:06

I have a problem for you. It was a high school problem I had. Never found a real formula for it.

What is a 1 digit number where the numbers before it add up to the same thing as some number of numbers after it?

6 is the answer because 1+2+3+4+5 = 7+8 (15)

What is a 2 digit number? A 3 digit number?

Is there a formula to find these numbers or is the only way to find out to test every sumation of number sequences and see? (I know there is a formula for sums of sequences but is there a way to quickly identify these kinds of numbers.)

Can you generate the first 15 numbers that have this property?

--Ken
Your Kung-Fu is not strong. -- 'The Core'

jhermiz

3564 Posts

Posted - 2004-07-18 : 02:29:11

quote:
Originally posted by kselvia

I have a problem for you. It was a high school problem I had. Never found a real formula for it.

What is a 1 digit number where the numbers before it add up to the same thing as some number of numbers after it?

6 is the answer because 1+2+3+4+5 = 7+8 (15)

What is a 2 digit number? A 3 digit number?

Is there a formula to find these numbers or is the only way to find out to test every sumation of number sequences and see? (I know there is a formula for sums of sequences but is there a way to quickly identify these kinds of numbers.)

Can you generate the first 15 numbers that have this property?

--Ken
Your Kung-Fu is not strong. -- 'The Core'

Hey Ken,

You cannot generalize something like this. You're just running into special cases such as 15=7+8. In fact there is too many inconsistances (5 digits on left, 2 on right to total 15, not good) to generalize this or prove it.

At least from my understanding I don't think I can generalize this.
Maybe you can / cannot but I don't see it.

Jon
www.web-impulse.com

Can you dig it: http://www.thecenturoncompany.com/jhermiz/blog/

Kristen
Test

22859 Posts

Posted - 2004-07-18 : 03:27:39

Ah, so I CAN use a tally table for this one? <g> but I only get the first 5 as my tally table only goes up to 8,000 :-(


SELECT	[Total before] = (S1.Number*(S1.Number+1))/2,
	[Number] = S1.Number+1,
	[Limit] = S1.Number+S2.Number+1
FROM	Tally S1,
	Tally S2
WHERE	    (S1.Number*(S1.Number+1))/2 = (S1.Number+1)*S2.Number+((S2.Number*(S2.Number+1))/2)
	AND S2.Number <= S1.Number / 2 	-- Prevent it taking forever!
	AND S1.Number < 1000		-- Prevent it taking forever!
ORDER BY S1.Number

Kristen

kselvia
Aged Yak Warrior

526 Posts

Posted - 2004-07-18 : 03:39:41

Sorry for hijacking your post Corey!

Good one Kristen. I was trying to do it myself but I was using a correlated subquery and couldn't figure it out. I wrote a BASIC program to solve it years ago and it took about a day to solve for a 5 digit number before the sum became larger than a double could hold. Interestingly, there was only 1 solution for each digit count.

--Ken
Your Kung-Fu is not strong. -- 'The Core'

Arnold Fribble
Yak-finder General

1961 Posts

Posted - 2004-07-18 : 04:30:03

[code]
SELECT x, n
FROM (
SELECT n, CAST(FLOOR(SQRT(x2)) AS bigint) AS x, x2
FROM (
SELECT n, (CAST(n AS bigint)*n+n)/2 AS x2
FROM Numbers
WHERE n > 0
) AS A
) AS A
WHERE x*x = x2
ORDER BY x
[/code]

BTW, This link might be of interest
http://www.research.att.com/projects/OEIS?Anum=A001109

kselvia
Aged Yak Warrior

526 Posts

Posted - 2004-07-18 : 04:51:24

I look at that and suppose you wrote it out just as it is, and well, that's just scary.

--Ken
Your Kung-Fu is not strong. -- 'The Core'

Arnold Fribble
Yak-finder General

1961 Posts

Posted - 2004-07-18 : 05:16:09

Well, a few back of envelope scribblings, and an attack of conscience on the floating point accuracy...
But it's still a damned slow way: it turns out that there's a recurrence to calculate square triangular numbers!
Not very set-based, I'm afraid:


DECLARE @STn2 AS bigint, @STn1 AS bigint, @STn AS bigint
SET @STn2 = 0
SET @STn1 = 1
DECLARE @i AS int
SET @i = 0
WHILE @i < 12 BEGIN
  SET @i = @i + 1
  SET @STn = 34*@STn1 - @STn2 + 2
  PRINT @STn
  SET @STn2 = @STn1
  SET @STn1 = @STn
END

Oh, better yet, there's a recurrence for the square root of that too:


DECLARE @a3 AS bigint, @a2 AS bigint, @a1 AS bigint, @a AS bigint
SET @a3 = 0
SET @a2 = 1
SET @a1 = 6
DECLARE @i AS int
SET @i = 0
WHILE @i < 23 BEGIN
  SET @i = @i + 1
  SET @a = 7*(@a1 - @a2) + @a3
  PRINT @a
  SET @a3 = @a2
  SET @a2 = @a1
  SET @a1 = @a
END

Much prettier in Haskell: lovely lazy evaluation (ideal for a lazy Sunday), infinite lists and proper bigints:


-- Square Triangular numbers
st = 0:1:(zipWith (\a b -> 34*a-b+2) (drop 1 st) st)
-- Their square roots (i.e. index in square numbers)
sts = 0:1:6:(zipWith3 (\a b c -> 7*(a-b)+c) (drop 2 sts) (drop 1 sts) sts)
-- index in triangular numbers
stt = 0:1:8:(zipWith3 (\a b c -> 7*(a-b)+c) (drop 2 stt) (drop 1 stt) stt)
-- put them all together:
stall = zip3 sts stt st
-- take the 10000th value
st10000 = stall !! 10000

Seventhnight
Master Smack Fu Yak Hacker

2878 Posts

Posted - 2004-07-18 : 21:25:24

Sorry I disappeared, but I'm glad someone brought more fun to the table (thanx Ken!). I will have to try and decipher arnold's code... I will see if I can come up with a good puzzler...

Corey

RyanRandall
Master Smack Fu Yak Hacker

1074 Posts

Posted - 2006-07-26 : 12:58:11

quote:
p(9594) = ???

I make it 100003

--calculation
select max(i) from (
    select top 9594 i from (
        select i from dbo.F_TABLE_PRIME(110000) union select 1) a
    order by i) b

F_TABLE_PRIME is here:
http://www.sqlteam.com/forums/topic.asp?TOPIC_ID=69646

Ryan Randall
www.monsoonmalabar.com London-based IT consultancy

Solutions are easy. Understanding the problem, now, that's the hard part.

Arnold Fribble
Yak-finder General

1961 Posts

Posted - 2006-07-26 : 13:24:33

Yes, but what's the 10000th square triangular number?

RyanRandall
Master Smack Fu Yak Hacker

1074 Posts

Posted - 2006-07-26 : 14:21:56

--calculation
declare @k int
set @k = 10000
select power((power(1 + sqrt(2.0), 2 * @k) - power(1 - sqrt(2.0), 2 * @k)), 2) / 32

/*result
1.53298e+15143
*/

Ryan Randall
www.monsoonmalabar.com London-based IT consultancy

Solutions are easy. Understanding the problem, now, that's the hard part.

Arnold Fribble
Yak-finder General

1961 Posts

Posted - 2006-07-27 : 07:57:16

quote:
Originally posted by RyanRandall
1.53298e+15143

Strange, I make it
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Kristen
Test

22859 Posts

Posted - 2006-07-27 : 08:57:54

It makes be feel so inadequate when you quote those things from memory Arnold

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