one version of the "top 300" sequences, and extra-terrestrial communication.

[Antti Karttunen]

N. J. A. Sloane wrote:

>Dear Seqfans,
>
>Michael Somos sent me a list of the "top 300" sequences (at my request).
>
>This is by no means meant to be a scientific judgement.
>It is based on personal preferences, and sorted according to
>the length of the entry.
>
>The "merit" increases as you do down the list,
>ending of course with the Catalan numbers.
>
>People may find it interesting, and it could be a guide
>for which sequences should have b-files.
>(Some of these already have b-files.)
>
>Neil
>
>  
>
...
...
...

>A000142
>A001006
>A000984
>A001003
>A001045
>A000217
>A000040
>A000041
>A000110
>A000045
>A000108
>:e
>
>  
>
If there are other OEIS'es on the extra-solar planets (or dwarf planets...),
then I think their users will rank this high end about the same way.
(Although, probably they have proportionaly less base-10 sequences
in their databases...)

This reminds me also of this Linas Vepstas' project of
"A Better Way to Search for ETI Signals".

http://www.linas.org/theory/seti.html

My "slightly improved idea" is to use the set of quadratic residues (or 
non-residues)
of a prime, padded with an extra bit, as the modulating pseudo-random
sequence, if it is just random enough for the purpose. (So naturally
tying a specific PRN-sequence to a particular prime, instead of trying
to find it among the multitude of LFSR-generated sequences.)
Furthermore, this suggests a few novel sequences, e.g. a sequence
giving primes whose "quadratic residues/non-residues vectors" match
successively better and better to the binomial distribution.
(I hope I understood correctly, that this is what is needed...)
(Preferably computed in a "cyclical fashion", because it is essentially
binary _necklaces_ that are used in PSK-modulation, as fas as I understand
the article.)
I think this will automatically favour primes that are near to some
power of 2.

Included is my original haphazardous notes on the subject. (As a HTML-file).
Some sequences just popped up, and are quite far-fetched for this 
application.
Anyway, the problem seems to be this: you have first to search the 
"platonic space"
(the right prime), before you can even starting to search the "physical 
space".

And after all, there are _some_ use for all these "intersection of 
A000040 and Ayyyyyy"
kind of sequences.


Terveisin,

Antti



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