[seqfan] Re: Use of Easy keyword
David Wilson
davidwwilson at comcast.net
Tue Dec 6 01:53:28 CET 2011
I find the "hard" keyword useful. It more or less says that it would be
a challenge to compute many
more terms than are already in the OEIS.
I find "easy" less useful. It has many potential meanings: easy to
understand, easy to write (a
possibly inefficient) program, easy to obtain small elements, easy to
obtain large elements, etc.
From a conceptual standpoint, simple functions of the n's prime
factorization are easy. Also, given
that OEIS b-files rarely exceed 10^4 elements, it would be easy to
extend the OEIS database for
these functions. For example, A000010(n) = phi(n) is a simple function
of the prime factorization,
and the b-file includes a whopping 10^5 elements, still, a
straightforward computer program
could churn out values of phi(n) up to 10^10 almost continuously.
Conceptually, A000142(n) = n! has an extremely simple definition that
does not involve factorization.
However, in computing n!, one runs into problems far sooner than with
most simple functions of
the prime factorization of n. Still, it would be quite easy to extend
the OEIS database, which only
goes up to a(100).
The only real use I could see for "easy" would be as an invitation to
extend the sequence. But we
already have "more" for that, and there are many "easy" sequences that
don't bear extension
because they are reasonably complete. I would move that the "easy"
keyword be deprecated
on the grounds of ill-definition and uncertain utility.
If there is any value to the easy keyword, I would say that "easy" is an
invitation for the OEIS to
support programmatic generation of sequences. If the OEIS supported,
say, JavaScript or PHP
programs that could be run client-side to generate sequence values, then
numerous bulky b-files
could be dispensed with in favor of short programs. Just saying.
On 12/3/2011 12:03 PM, Ed Jeffery wrote:
> Seqfans,
>
> I keep running across sequences in OEIS with simple
>
> descriptions or definitions but which, in one way
>
> or another, depend on factorization of n. The problem
>
> of factorization is still hard (or intractable) for
>
> arbitrarily large n, but many of these sequences have
>
> been given the EASY keyword which seems to be a bit
>
> misleading. Should this keyword be dropped for such
>
> sequences?
>
>
> Ed Jeffery
>
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