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Generating a specific list of intsgers


On Saturday, August 25, 2018 at 9:46:21 AM UTC-5, Richard Damon wrote:
> On 8/25/18 10:27 AM, Dennis Lee Bieber wrote:
> > On Sat, 25 Aug 2018 03:56:28 +0000 (UTC), Steven D'Aprano
> > <steve+comp.lang.python at pearwood.info> declaimed the following:
> >
> >> On Fri, 24 Aug 2018 14:40:00 -0700, tomusatov wrote:
> >>
> >>> I am looking for a program able to output a set of integers meeting the
> >>> following requirement:
> >>>
> >>> a(n) is the minimum k > 0 such that n*2^k - 3 is prime, or 0 if no such
> >>> k exists
> >>>
> >>> Could anyone get me started? (I am an amateur)
> >>
> >> That's more a maths question than a programming question. Find out how to 
> >> tackle it mathematically, and then we can code it.
> > 	I'd want more punctuation in that just to ensure I'm interpreting it
> > properly -- I'm presuming it is meant to be parsed as:
> > 		(n * (2 ^ k)) - 3
> >
> > 	Suspect this needs to be attacked in the reverse direction -- generate
> > a list of primes, add 3, determine if it is a multiple of powers of two.
> > Though in that case, k = 1 would fit all since if it is a multiple 2^2 (4)
> > it would also be a multiple of 2^1 (2), for all greater powers of 2..
> >
> > 	prime 5
> > 	+ 3 => 8
> > 	log_2 8 => 3			<<< integral k
> > 	8 => 1 * (2 ^ 3)
> > 		 2 * (2 ^ 2)
> > 		4 * (2 ^ 1)
> >
> > n=4, k=1
> >
> > 	OTOH, if it is supposed to be (n*2) ^ k, or even worse (n*2) ^ (k-3)
> > the solution becomes more difficult.
> >
> >
> I think the issue is given n, find k.
> 
> a(1): 1*2-3=-1 no, 1*4-3=1 no, 1*8-3 - 5 YES, a(1) = 3
> 
> a(2) 2*2-3 = 1, no 2*4-3=5 YES a(2) = 2
> 
> a(3) 3*2-3 - 3 YES, a(3) = 1
> 
> and so on.
> 
> One path to solution is to just count up the k values and test each
> result for being prime, except that will never return 0 to say no such k
> exists. That will require some higher level of math to detect (or an
> arbitrary cap on k, and we say we can say 0 if the only k is too big,
> but with big nums, that would be VERY large and take a very long time.
> 
> -- 
> Richard Damon
Here is a sample output:	
3, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 3, 1, 0, 1, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 1, 0, 3, 1, 0, 1, 2, 0, 1, 1, 0, 5, 2, 0, 1, 1, 0, 2, 1, 0, 3, 1, 0, 1