[seqfan] updated list of formulas (conjectures)
Simon Plouffe
simon.plouffe at gmail.com
Mon Feb 14 00:09:22 CET 2011
Hello,
I updated the list of conjectures, there are
over 64789 formulas (36511 unique sequences)
are represented.
Here is the header of the file :
The score is included in the file as a mean to know if
the formula is somewhat reliable.
Best regards,
Simon Plouffe
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Conjectured formulas of the OEIS by Simon Plouffe as of Feb 13. 2011
There are 36511 unique sequence and more than 64789 expressions.
Score = log(# of terms)/(length of sequence)/(length of the sequence).
If the score is high the reliability of the formula is good.
A score near 1 is not good, a score of 20+ is excellent.
Some formulas are in double for many reasons, the sign or the factorization
of the expression makes a change in length. The intention of the author
is to keep the list as clean as possible, with time it will be done...
These formulas are suggested, most of them are the true ones, in some
cases the formula found automatically are better than the original
reference.
Some formulas are false positives, in some rare cases, even false
the formula found is sometimes as interesting as the original.
See A063003 for an example.
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OEIS # Score Formula Type
---------------------------------------------------------------------------------------
A000008 15.3971 1/(x^4-x^3+x^2-x+1)/(x+1)^2/(x^4+x^3+x^2+x+1)^2/(x-1)^4 ogf
A000008 76.9855 1+x+x^4+x^9 ogf_with_Euler_Transform
A000009 91.2781 1/(1-x^2) ogf_with_Euler_Transform
A000012 123.912 -1/(x-1) ogf
A000023 46.1177 (1-2*x)*f(x)+(1-x)*f(x)^2 lgdegf
......
......
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