MathDB

Let

a_0

a_1

a_2

\dots

be an infinite sequence of real numbers such that

a_0 = \frac{4}{5}

and

a_{n} = 2 a_{n-1}^2 - 1

for every positive integer

n

. Let

c

be the smallest number such that for every positive integer

n

, the product of the first

n

terms satisfies the inequality

a_0 a_1 \dots a_{n - 1} \le \frac{c}{2^n}.

What is the value of

100c

, rounded to the nearest integer?

20