[seqfan] Re: 3-sequences relations using Robert Gerbicz's seeker.c
Charles Greathouse
charles.greathouse at case.edu
Tue Aug 24 04:01:29 CEST 2010
That does sound interesting. But I think it's infeasible for other
reasons: the human time needed to sift through the resulting
sequences.
If (extrapolating) there are a million 3-sequence relationships
between 200,000 sequences, then we'd expect to the order of a hundred
million 4-sequence relationships between 200,000 sequences.
In fact, even just the 3-sequence relations seem hard to analyze. If
there are 500 active SeqFans members (surely an overestimate) then
each would need to check 2000 sequence relations. Perhaps half would
be trivial and anther quarter could be dismissed without much work,
but that's still 500 difficult relations per person. 50 I could
imagine; 500 would be too many to ask. 50,000 seems entirely more
than a person could reasonably check.
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Mon, Aug 23, 2010 at 7:23 PM, Robert Gerbicz
<robert.gerbicz at gmail.com> wrote:
> 2010/8/23 Georgi Guninski <guninski at guninski.com>
>
>> using Robert Gerbicz's seeker.c [1] [2] (modified for speed version) i
>> looked for inter-oeis relations involving 3 sequences. results:
>>
>> in about 90 minutes, about 50 000 sequence analyzed on a singe core:
>>
>> 167284 relations found (sic, false positives)
>>
>> the first 30 terms of pruned "stripped" file were used, a lot of false
>> positives due to insufficient number of terms.
>>
>> the database in oeis format is at:
>> http://stefan.guninski.com/seq/seekjn1
>>
>> searchable web interface:
>> http://stefan.guninski.com/cgi/oeis-seekjn1.cgi?q=%25F
>>
>> (use +Anumber to search for a sequence)
>>
>> search for the primes:
>> http://stefan.guninski.com/cgi/oeis-seekjn1.cgi?q=%2BA000040
>>
>> search for euler_phi:
>> http://stefan.guninski.com/cgi/oeis-seekjn1.cgi?q=%2BA000010
>>
>> some random results (might be wrong):
>>
>> %F A108954 =A000010-A077150
>> %F A000040 =A090417-A031165
>>
>> [1] http://list.seqfan.eu/pipermail/seqfan/2010-August/005615.html
>> [2] http://list.seqfan.eu/pipermail/seqfan/2010-August/005617.html
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
> It would be possible to generate (or only count) all 4-sequences relations
> in about the same amount of time (by a new code), unfortunately to do this
> in Ram is impossible, but by using harddisk is possible. So to find all s1
> op1 s2 op2 s3 op3 s4 = 0 relation (where op={+,-,*,/}), for example:
> s1-s2*s3*s4=0 or s1*s2/s3-s4=0.
>
> The idea is the same s1 OP1 s2 = s3 OP2 s4, generate both sides then do a
> binary search.
>
> "A108954 =A000010-A077150"
>
> It is actually true, proof: eulerphi(n)=#{m: 1<=m<=n and gcd(n,m)=1}=#{m:
> n+1<=m<=2n and gcd(n,m)=1} because if m=n+i then gcd(n+i,n)=gcd(i,n). But in
> A077150 we take only m values that is composite. So for the remaining
> numbers: if m is prime then gcd(n,m)=1, since m>n and m is prime, and there
> are primepi(2n)-primepi(n) prime numbers in (n,2n] interval. So
> A108954+A077150=A000010 what is needed.
>
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>
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