In this section we describe the results of a computation of the beta expansions for the
11836 Salem numbers of degree 6 and trace at most 15. The complete expansion was
obtained except in 80 cases. The distribution of the pairs for these numbers
is quite remarkable. For the most part there is a great deal of regularity, and the
values of m and p are quite small: for all but 199 of the numbers surveyed, both
m < 1000 and p < 1000. For 9609 of the numbers (81% of the total) we
have m = 1, but, in contrast to the degree-4 situation, larger values of m do
occur with a certain regularity. However, among the remaining 199 cases, there are
at least 79 for which and at least two for which .