PARI's commands - Page 42

science_man_88 · 2010-08-14, 19:08

Quote:

Originally Posted by CRGreathouse

Thanks, axn. I tend to forget that not everyone is a computer programmer.

I program a bit (pari only recently) just never heard the term.

science_man_88 · 2010-08-14, 19:12

A006516 and A019279 is there a similar way to get these if so once we find a way to get one of the three to work only for the correct indexes we can apply it to the other 2.

CRGreathouse · 2010-08-14, 19:13

Quote:

Originally Posted by science_man_88

I program a bit (pari only recently) just never heard the term.

Maybe I should have used the term dynamic programming instead? It just seemed a little highfalutin when all I meant was "don't redo what you already did".

CRGreathouse · 2010-08-14, 19:22

Quote:

Originally Posted by science_man_88

A006516 and A019279 is there a similar way to get these if so once we find a way to get one of the three to work only for the correct indexes we can apply it to the other 2.

A006516 is 2^2n-1 - 2^n-1, so let's look at
$\sum_{n=1}^{x-1}2^{2n-1}-2^{n-1}=\sum_{n=1}^{x-1}2^{2n-1}-\sum_{n=1}^{x-1}2^{n-1}=1/2\left(\sum_{n=1}^{x-1}4^n-\sum_{n=1}^{x-1}2^n\right)=1/2\left(\frac{4^x-4}{4-1}-\frac{2^x-2}{2-1}\right)=\frac{2^{2x-1}-2}{3}-\frac{2^{x-1}-1}{1}$

Can you take this the rest of the way?

science_man_88 · 2010-08-14, 19:32

$\frac{2^{2x-1}-2}{3}-\frac{2^{x-1}-1}{1}$

3 times the first gives:

$2^{2x-1}-2$ add 1 and you get $2^{p=2x-1}-1$

so both can become Mersenne numbers.

science_man_88 · 2010-08-14, 19:46

the second term's numerator could be turned into a mersenne prime but I doubt that helps the other numerator or fraction.

CRGreathouse · 2010-08-14, 20:09

Quote:

Originally Posted by science_man_88

the second term's numerator could be turned into a mersenne prime but I doubt that helps the other numerator or fraction.

You should be paying attention to the first term, I think, since that's about one-third of the number you want.

science_man_88 · 2010-08-14, 20:17

Quote:

Originally Posted by science_man_88

the second term's numerator could be turned into a mersenne prime but I doubt that helps the other numerator or fraction.

I'm an idiot the second term's numerator is a Mersenne where p=x-1

times the first by 3 and add 1 to the -2 to get -1 and we get another Mersenne with p=2x-1. so these can be transformed to Mersenne numbers since we have an equation maybe it's time to apply it.

CRGreathouse · 2010-08-14, 20:19

Quote:

Originally Posted by science_man_88

times the first by 3 and add 1 to the -2 to get -1 and we get another Mersenne with p=2x-1. so these can be transformed to Mersenne numbers since we have an equation maybe it's time to apply it.

Write out the full equation first and make sure it's right.

science_man_88 · 2010-08-14, 20:28

$\frac{2^{2x-1}-2}{3}-\frac{2^{x-1}-1}{1}$

3 times the first gives:

$2^{2x-1}-2$ add 1 and you get $2^{p=2x-1}-1$

so both can become Mersenne numbers

CRGreathouse · 2010-08-14, 20:31

I meant with the sum. $2^{2x-1}-1=2^{2x-1}-1$ is a boring equation.

2010-08-14, 19:32	#456
science_man_88 "Forget I exist" Jul 2009 Dumbassville 20300₈ Posts	$\frac{2^{2x-1}-2}{3}-\frac{2^{x-1}-1}{1}$ 3 times the first gives: $2^{2x-1}-2$ add 1 and you get $2^{p=2x-1}-1$ so both can become Mersenne numbers. Last fiddled with by science_man_88 on 2010-08-14 at 20:27

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2010-08-14, 19:12	#453
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶×131 Posts	A006516 and A019279 is there a similar way to get these if so once we find a way to get one of the three to work only for the correct indexes we can apply it to the other 2.

2010-08-14, 19:46	#457
science_man_88 "Forget I exist" Jul 2009 Dumbassville 10000011000000₂ Posts	the second term's numerator could be turned into a mersenne prime but I doubt that helps the other numerator or fraction.

2010-08-14, 20:28	#461
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶×131 Posts	$\frac{2^{2x-1}-2}{3}-\frac{2^{x-1}-1}{1}$ 3 times the first gives: $2^{2x-1}-2$ add 1 and you get $2^{p=2x-1}-1$ so both can become Mersenne numbers

2010-08-14, 20:31	#462
CRGreathouse Aug 2006 3×1,993 Posts	I meant with the sum. $2^{2x-1}-1=2^{2x-1}-1$ is a boring equation.