[seqfan] Re: Extending the superseeker

Georgi Guninski guninski at guninski.com
Fri Aug 20 14:23:50 CEST 2010


very nice and fast program thanks!

looks like this will be a useful feature to add (especially if the examined sequence |s| doesn't start with the right offset):

s[n]=s1[n+k1]+s2[n+k2]
where k1,k2 are small, possibly negative (may need to drop first terms of |s|).

btw, does seeker.c have a license?


On Sat, Aug 14, 2010 at 01:05:54AM +0200, Robert Gerbicz wrote:
> Currently the superseeker is unable to find identities such that for a given
> s sequence:
> s1+s2=s
> s1-s2=s
> s1*s2=s
> s1/s2=s
> where s1 and s2 are existing A sequences. But we can do it very quickly,
> just sort the A sequences in lexicographic order and do binary search if you
> fix s2. The only weak point is that finding s1*s2=s is only possible (in
> this fast way) if s1 (or s2) has got only non-zero terms (this is true for
> example if s has got no zero terms), because the solution of a*x=b is not
> unique if a=b=0.
> 
> Note that the code prints the solutions only if both s1 and s2 has got no
> less terms than s.
> 
> See my seeker.c that finds all these type of identities. You need gmp
> program (and currently about 210 MB of Ram). The program needs the stripped
> file from the main page (download stripped.gz and extract it).
> 
> Just an example for 4 sequences:
> 
> Read sequences from stripped file.
> Number of sequences=178308
> Sort is done.
> Give the integer sequence, terms seperated by commas or spaces (one sequence
> per line)
> 4 7 10 19 35 83 210 591 1699 5021 14905 44556 133254 399340
> // Read sequence has got 14 terms.
> =A001998+A072716
> Number of found identities=1, time=1 sec.
> 
> -4 -55 -90 -124 -171 -193 -204 -226 -279 -313 -366 -400 -429
> // Read sequence has got 13 terms.
> =A045506-A051227
> Number of found identities=1, time=1 sec.
> 
> 1 4 12 98 627 7800 80769 1337670 16365165 306808450 4093063920
> // Read sequence has got 11 terms.
> =A006384*A007481
> Number of found identities=1, time=1 sec.
> 
> 4 0 3 5 12 24 45 180 455 928 1809 9510
> // Read sequence has got 12 terms.
> =A005589*A005043
> =A052360*A005043
> Number of found identities=2, time=1 sec.

> 
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> 
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