Journal of Integer Sequences, Vol. 11 (2008), Article 08.4.1 |

Department of Mathematics

University of Illinois

Urbana, IL 61801

USA

**Abstract:**

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.

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(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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