MathDB

Let

\mathbb{Z}_{\ge 0}

denote the set of nonnegative integers.
Define a function

f:\mathbb{Z}_{\ge 0} \to\mathbb{Z}

with

f\left(0\right)=1

and

f\left(n\right)=512^{\left\lfloor n/10 \right\rfloor}f\left(\left\lfloor n/10 \right\rfloor\right)

for all

n \ge 1

. Determine the number of nonnegative integers

n

such that the hexadecimal (base

16

) representation of

f\left(n\right)

contains no more than

2500

digits.
Proposed by Tristan Shin

Problem Statement