Representation of Integers by Near Quadratic Sequences
120 rue de Charonne
Department of Mathematics
Pennsylvania State University
25 Yearsley Mill Road
Media, PA 19063
Following a statement of the well-known Erdos-Turán conjecture,
Erdos mentioned the following even stronger conjecture: if the
-th term an
of a sequence A
of positive integers is bounded by
for some positive real constant
the number of representations of n
as a sum of two terms
is an unbounded function of n
. Here we show that if an
(or from a quadratic polynomial with rational
)) by at most
then the number of
representations function is indeed unbounded.
Full version: pdf,
Received July 19 2012.
revised version received October 14 2012.
Published in Journal of Integer Sequences, October 23 2012.
Journal of Integer Sequences home page