\begin{definition}[Definition:Earthworm Sequence]
The '''earthworm sequence''' is the integer sequence $\sequence {h_n}$ defined as follows.
Let $h: \Z \to \Z$ be the mapping defined as:
:$\forall a \in \Z: \map h a = 2 a \pmod {100}$
Then:
:$h_n = \begin {cases} x: x \in \set {10, 11, \dotsc, 99} & : n = 0 \\ \map h {n - 1} & : n > 0 \end {cases}$
That is:
:$h_0$ is an arbitrary integer between $10$ and $99$
:$h_n$ is the result of multiplying the previous term in the sequence by $2$ and keeping only the last two digits.
\end{definition}