  The Stern sequence (s(n)) is defined by s(0) = 0, s(1) = 1, s(2n) = s(n),
s(2n+1) = s(n) + s(n+1). Stern showed in 1858 that gcd(s(n),s(n+1)) = 1, and
that for every pair of relatively prime positive integers (a,b), there exists a
unique n so that s(n) = a and s(n+1) = b. We show that, in a strong sense, the
average value of s(n)/s(n+1) is 3/2, and that for all d, (s(n),s(n+1)) is
uniformly distributed among all feasible pairs of congruence classes modulo d.
More precise results are presented for d = 2 and 3.
