MathDB

Given an integer

m

, define the sequence

\left\{a_{n}\right\}

as follows: a_{1}\equal{}\frac{m}{2},\ a_{n\plus{}1}\equal{}a_{n}\left\lceil a_{n}\right\rceil,\textnormal{ if }n\geq 1 Find all values of

m

for which

a_{2007}

is the first integer appearing in the sequence. Note: For a real number

x

\left\lceil x\right\rceil

is defined as the smallest integer greater or equal to

x

. For example, \left\lceil\pi\right\rceil\equal{}4, \left\lceil 2007\right\rceil\equal{}2007.

Problem Statement