[seqfan] Re: Looking back at your earliest sequences

Peter Luschny peter.luschny at gmail.com
Tue Mar 12 22:44:25 CET 2013


If I remember right my first sequence submitted was A103294.
The references given there (R. K. Guy, J. C. P. Miller and B. Wichmann)
tell the mathematical background. Basically it is build around
Sloane's and Plouffe's A004137, which was the link which made
things interesting enough to start. The name of A004137 is
"Maximal number of edges in a graceful graph on n nodes".

But the actual start was a discussion in the newsgroup de.sci.mathematik,
a long and vivid discussion with many contributors (I remember Rainer
Rosenthal, Klaus Nagel and Hugo Pfoertner) which went on for several
months and was much fun.

Part of this fun was that in the course of the discussion a simple
interpretation
of A004137 was found in terms of rulers. On the OEIS-wiki (*) you find an
introduction to this general type of rulers. Another source of the fun was that
A004137 is hard to compute (OEIS lists only 21 terms) and we all tried to find
more terms and better algorithms.

Today, nine years later, I think A004137 could be pushed further, perhaps a
good coder should give it another try. ('Cool multi-CPU parallel programming
optimizations' is just what is needed).

For me this is a success story of a newsgroup community. In June 2011
L. Egidi and G. Manzini wrote ("Spaced seeds design using perfect rulers"):

"The notion of perfect ruler has been studied by mathematicians for more
than sixty years (in earlier works rulers were called di
fference bases).
Here we recall the basic definitions using modern terminology".

Indeed this "modern terminology" was developed in this discussion
and layed out in A103294 through A103301 in 2005.

Peter

(*) http://oeis.org/wiki/User:Peter_Luschny/PerfectRulers



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