MathDB

Given a positive integer

n

, an allowed move is to form

2n+1

3n+2

. The set

S_{n}

is the set of all numbers that can be obtained by a sequence of allowed moves starting with

n

. For example, we can form

5 \rightarrow 11 \rightarrow 35

5, 11

and

35

belong to

S_{5}

. We call

m

and

n

compatible if

S_{m}

and

S_{n}

has a common element. Which members of

\{1, 2, 3, ... , 2002\}

are compatible with

2003

Problem Statement