[seqfan] Extending the superseeker
Robert Gerbicz
robert.gerbicz at gmail.com
Sat Aug 14 01:05:54 CEST 2010
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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