Choose a programming language. Choose a sequence prefix (in your example: 2, 3). Then consider all the programs that accept n as input and output a sequence of n numbers, such that the first numbers are always 2, 3. Now take the shortest of those programs. The sequence it produces is the "simplest".
If this sounds tedious to code, you could easily outsource via Odesk or something.
Choose a programming language. Choose a sequence prefix (in your example: 2, 3). Then consider all the programs that accept n as input and output a sequence of n numbers, such that the first numbers are always 2, 3. Now take the shortest of those programs. The sequence it produces is the "simplest".
If this sounds tedious to code, you could easily outsource via Odesk or something.