The tern sequence
s(
n) is defined by
s(0) = 0,
s(1) = 1,
s(2
n) =
s(
n),
s(2
n+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 ≥ 1. We show that in a strong sense, the
average value of these fractions is 3/2. We also show that
for
d ≥ 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.
Full version: pdf,
dvi,
ps,
latex
(Concerned with sequence
A002487.)
Received August 31 2008;
revised version received September 16 2008.
Published in Journal of Integer Sequences, September 16 2008.
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