Random Sequencing
Olivier Gerard
ogerard at ext.jussieu.fr
Mon Sep 16 09:58:18 CEST 2002
Dear Jon,
For this kind of musings which borders on the un-mathematical (since the average answer
of the OEIS does not depend on physics or mathematics but mainly
on OEIS history and its contributors' humanity, ability and creativity), you
should do it yourself (number of answers is limited in the public
version of the OEIS since this is a shared resource, and something
like 1,2,3 brings something like 8600 potential answers):
- download the whole OEIS files (around 46 Mo, 70+ files)
- use a programming language with a random generator you
trust (this is rare) and an interface to a full text search (such as unix
grep -c) to make sufficiently many sample searches in the files.
Since your space is (10^2)^3 = 1 million triples you will have
to find a good and relevant sampling too.
- analyze the results.
- ask Neil or me before posting them here
It is likely -- if you succeed in eliminating the innumerable biases of
such a study, that you will at best come up with something close to Richard Guy's
strong laws of small numbers (basically, there are too few small numbers
for all the mathematical properties, classes or sequences one can
think about).
R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.
R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), no. 1, 3-20.
Good luck,
Olivier Gérard
PS: there are at least 4700 occurences of the sub sequence 0,1,2
in the OEIS and currently none of 0,47,99. This gives you
an idea of the spread of your sample.
Le 15, Jon Perry écrivait:
> Suppose I was to type a random integer sequence of say 3 integers<100 into
> the lookup box.
>
> How many sequences would be returned?
>
> Jon Perry
> perry at globalnet.co.uk
> http://www.users.globalnet.co.uk/~perry/maths
> BrainBench MVP for HTML and JavaScript
> http://www.brainbench.com
>
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