Monday, July 15, 2013 11:30 pm
-
11:30 pm
EDT (GMT -04:00)
J.C. Saunders, Department of Pure Math, University of Waterloo
"Sums of Digits in q-ary expansions Part 2"
Let
sq(n)
denote
the
sum
of
the
digits
of
a
number
n
in
base
q.
For
example,
s2(n)
represents
the
number
of
1s
in
the
binary
expansion
of
n.
In
1978,
Kenneth
B.
Stolarsky
showed
that
lim
inf
n!1
s2(n2)
s2(n)
=
0
using
bounds
obtained
from
analytical
methods.
In
the
last
presentation
we
showed
that
the
ratio
s2(n2)
s2(n)
can
indeed
hit
every
positive
rational
number.
In
this
presentation,
we
show
that
the
same
is
true
for
this
ratio
in
general
base
q,
that
is
sq(n2)
sq(n)
:
n
2
N
=
Q+:
for
all
q
2.
If
time
permits,
we
will
also
look
at
powers
with
certain
fractional
exponents
to
derive
similar
conclusions.