Summary: The tern 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 every positive rational number $a/b$ occurs exactly once in the form $s(n)/ s(n+1)$ for some $n \ge 1$. We show that in a strong sense, the average value of these fractions is 3/2. We also show that for $d \ge 2$, the pair $(s(n), s(n+1))$ is uniformly distributed among all feasible pairs of congruence classes modulo $d$. More precise results are presented for $d = 2$ and 3.

05A15, 11B37, 11B57, 11B75

stern sequence, enumerations of the rationals, stern-brocot array, dijkstra's "fusc" sequence, integer sequences mod m