new keyword: probation

[Hugo Pfoertner]

"N. J. A. Sloane" wrote:
> 
> Thanks to everyone who replied to my request for advice
> 
> There were many excellent suggestions
> 
> I'm going to try the following: sequences of doubtful value
> will get a new keyword:  probation.  I hope that the associate editors
> and other seqfans will look at these from time to time,
> and either edit them or suggest that they be removed.
> 
> After a while, if noone votes for keeping them, they will be removed.
> 
> Let's try this and see how it works.
> 
> To find these, search for  keyword:probation
> 
> Neil

My first experience with the "on probation"-sequences leads me (as
expected) into a dilemma. Most of the sequences by the two (long-known
for low signal/noise ratio) submitters are really candidates for
/dev/null or its Windoze equivalent.

But after reading http://www.research.att.com/~njas/sequences/A115598
Interesting polynmial coefficient expansion of (x - 1)/(x^(10) + x^9 -
x^7 - x^6 - x^5 - x^4 - x^3 + x + 1):Salem Lehmer (1933).
(does the use of the word "interesting" in the title make a sequence
interesting?) 
I started to search for "salem polynomial" and found S. Plouffe's
http://www.research.att.com/~njas/sequences/A029826
and tons of other artificial Bagula sequences.

Further search brought up
http://www.research.att.com/~njas/sequences/A073011 and
http://www.research.att.com/~njas/sequences/A070178

Since both didn't help me to understand the connection between the Salem
constant and the Lehmer polynomial, I searched on the web and found the
web pages of Michael Mossinghoff.

But instead of editing Bagula's artificial extensions I found it much
more useful to make comments on the existing pages A070178 and A073011:

%I A073011
%S A073011 1, 1, 7, 6, 2, 8, 0, 8, 1, 8, 2, 5, 9, 9, 1, 7, 5, 0,
%C A073011 The Salem Constant given here is the smallest known value of
Mahler's measure M(f)=abs(a_d)*Product_{k=1..d}max(1,abs(b_k)) of a
polynomial f(x)=sum_{k=0..d}(a_k*x^k)=a_d*Product_{k=1..d}(x-b_k). The
minimum occurs for Lehmer's polynomial (coefficients A070178)
L(x)=x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1 with M(L)=1.1762808...

New links to Lehmer's Problem and Salem Numbers, X-Ref to Coefficients
of Lehmer's polynomial.
%H A073011 Michael Mossinghoff, <a
href="http://oldweb.cecm.sfu.ca/~mjm/Lehmer/">Lehmer's Problem.</a>
%H A073011 Michael Mossinghoff, <a
href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small
Salem Numbers.</a>
%H A073011 Eric Weisstein's World of Mathematics, <a
href="http://mathworld.wolfram.com/SalemConstants.html">Salem
Constants.</a>
%Y A073011 Cf. A070178 [Coefficients of Lehmer's polynomial].
%O A073011 1
%K A073011 ,cons,nonn,
%A A073011 Hugo Pfoertner (hugo at pfoertner.org), Mar 12 2006

%I A070178
%S A070178 1, 1, 0, -1, -1, -1, -1, -1, 0, 1, 1
%C A070178 Mahler's measure M(f) of a polynomial f is defined to be the
absolute value of the product of those roots of f which lie outside the
unit disk, multiplied by the absolute value of the coefficient of the
leading term of f. Of all polynomials with integer coefficients,
Lehmer's 10th degree polynomial produces the smallest known M(f), given
in A073011.
%H A070178 Michael Mossinghoff, <a
href="http://oldweb.cecm.sfu.ca/~mjm/Lehmer/">Lehmer's Problem.</a>
%Y A070178 Cf. A073011 [Mahler's measure of Lehmer's polynomial].
%O A070178 1
%K A070178 ,fini,full,sign,
%A A070178 Hugo Pfoertner (hugo at pfoertner.org), Mar 12 2006

Without Bagula's A115598 (which I still consider to be uninteresting) I
probably would never have heard of Salem Numbers. Does this alone
justify A115598's permanent inclusion into the database? Something
similar also applies to J vos Post's countless submissions. Some of them
include interesting literature references, e.g.
http://www.research.att.com/~njas/sequences/A115973 , but in most cases
the sequence is nearly unrelated to the references. JVP seems to use the
references, links and X-refs to core sequences only as "decoration" to
make his stuff look more important. Sometimes his collections might
inspire some thoughts, but in most (or all?) cases a few carefully added
comments, X-refs to existing sequences or extensions of the index might
serve the same purpose with much less parasitic noise.

Hugo Pfoertner