"Provable" Sierpinski and Riesel numbers

[David Wilson]

Recently, I commented that certain OEIS sequences related to Sierpinski and
Riesel numbers
appeared to be (at least mildly) inconsistent with definitions of Sierpinski
and Riesel numbers
from other sources.  Dean Hickerson pointed out to me that these
inconsistencies were for the
most part innocuous.

However, I did suggest that we create sequences of "provable" Sierpinski and
Riesel numbers.
By "provable", I mean provable by the standard method, that is, given a
candidate
Sierpinski/Riesel number k, to exhibit a periodic sequence d_k of nontrivial
divisors
with d_k_n | 2^n*k +- 1 (n >= 1).  The obvious conjecture is that every
Sierpinski/Riesel number
k has a corresponding periodic d_k (is this conjecture supported by a
probabilistic argument?).

The literature suggests that k = 78557(509203) is believed to be the least
Sierpinski(Riesel)
number.  I construe this to mean that no periodic d_k | 2^n*k +(-) 1 is
thought to exist for
smaller k.  I do not immediately see how d_k can be disproved for a given k,
except by
exhibiting a prime 2^n*k +- 1.  If such a disproof is possible, however, it
becomes possible
to construct conjectural sequences of Sierpinski/Riesel numbers which, IMHO,
should be
added to the OEIS.