[seqfan] 4-sequences relations: s1+s2=s3*s4 (first results)
Robert Gerbicz
robert.gerbicz at gmail.com
Thu Aug 26 12:50:48 CEST 2010
See some results:
https://docs.google.com/leaf?id=0B7pctl0ACPkjYTY3ZjM2NGQtMmJlMS00YmMxLTg1MmItODdjM2UyMTZmYjQz&hl=en
One of them is: A000910+A000579=A000389*A023447
This is an obvious identity:
5*binomial(n,6)+binomial(n,6)=binomial(n,5)*(n-5)
We consider only those sequences that has got at least 30 terms, not
constant sequence, and it has got less than 15 appearances of k as term in
the first 30 terms of the sequence (for k=-2,-1,0,1,2).
Doing this a lots of boring cases are avoided, for example: s+s=t*s is a
trivial identity true if for every i: s[i]*(2-t[i])=0 so s[i]=0 or t[i]=2,
it means that at least half of the terms of s or t is 0 or 2. And so we
don't find these relations.
Found 1034 relations for the first 10,000 lexicographic sequences in about 2
hours. Doing the whole project would need say about 160 hours (on the same
PC, 2.1 GHz Amd) for the 91,072 sequences (that qualify the above
restrictions). I won't do this, but anybody is welcome: it needs about 60GB
harddisk (and 2GB of Ram is enough). It is recommended to do this in a new
folder: the code generates about 160,000 temp files, however at the end all
of these are deleted. The results will be in seq4.txt file.
See my code:
https://docs.google.com/leaf?id=0B7pctl0ACPkjMGU4M2UxZGUtNjY1Yi00MWY2LTk0M2MtOWQ1ZDYxN2U4OWVl&hl=en
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