  We discuss the integer sequence transform $a \mapsto b$ where $b_n$ is the
number of real roots of the polynomial $a_0 + a_1x + a_2x^2 + \cdots + a_nx^n$.
It is shown that several sequences $a$ give the trivial sequence $b = (0,1,0,1,
0,1,\ldots)$, i.e., ${b_n = n \bmod 2}$, among them the Catalan numbers,
central binomial coefficients, $n!$ and $\binom{n+k}{n}$ for a fixed $k$. We
also look at some sequences $a$ for which $b$ is more interesting such as $a_n
= (n+1)^k$ for $k \geq 3$. Further, general procedures are given for
constructing real sequences $a_n$ for which $b_n$ is either always maximal or
minimal.
