[seqfan] Re: OEIS as a combinatorics castle
Eric Angelini
Eric.Angelini at kntv.be
Mon Dec 14 13:08:14 CET 2015
> Interesting musings and a point of view, Eric.
... thanks, Antti
> However, I think myself that the best "artificial laws"
> are those that feel most "natural" to me.
... all points of view and tastes are welcomed! The benefit
of an online digital database is that you can fulfill almost
everyone -- collectors, searchers, creators. The key is of
course the internal search engine, the way labels are given,
the data structure, the indexes, etc. I guess we will have
at some point in the future the possibility to make "voice
queries", or "sound queries", or "picture queries", or
"graph" comparisons, etc.
>(Sieve of Eratosthenes and Ludic numbers sieve) co-create
> something visually nice: https://oeis.org/A255422/graph
... indeed
> "Spiro-Fibonacci numbers" [...] where would you place it
> in your continuum of "natural" ... "artificial" laws?
... good point -- but the "natural/artificial" distinction
was emphasized by me only in the hope that more seqs would
be linked to each other based on their "building structure".
This is, what are the bricks and what are the laws that rule
the seq -- no matter if they are of interest "in the real
world".
This might of course be automatized -- and a seqs-generator
mixing data and recipes would probably produce chimeras and
nightmares -- but why not, if we have enough storage and
subtle search algorithms?
Naïve example of an online seq-generator
INTEGERS DATA SET (select one):
odd numbers
even numbers
triangular numbers
prime numbers
square numbers
pandigital numbers
palindromic numbers in base 2
terms belonging to A123456
terms not belonging to A123456
...
STARTING INTEGERS
a(1)= ...
a(2) = ...
a(3) = ...
RULE 1 (select one):
a(n) = a(n-1) + a(n-2)
a(n) = a(n-1) + a(n-2) + a(n-3)
a(n) = a(n-1) + |SQR(17*a(n-2)|
a(n) = a(n-1) + a(n-2) if a(n-2) is prime, else a(n) = a(n-1) + a(n-3)
...
RULE 2 (select one):
always extend the seq S with the smallest unused term so far in S
if the last term is divisible by 3, replace it by the closest next prime
...
RULE 3 (select one):
...
Best,
É.
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