I've recently come across the On-Line Encyclopedia of Integer Sequences and I'm completely fascinated by it; something about how easy integers are to grasp and yet how complex the sequences are. I find it intriguing and I'd love to be able to contribute to it. Naturally the sequences that are easier to come by have already been submitted and having only studied mathematics up to pre-calculus thus far I feel it is beyond my current abilities to discover something original.
And so my questions are:
- What would I require asides ingenuity to create/discover an original sequence?
- What topics would be helpful to study? Algebraic number theory?
- What topic should I study to build upon sequences & series that I've encountered in pre-calculus?
- Would I need to be able to programme? Or have a working knowledge of mathematica or another programming language?
Essentially, what knowledge would I require that would allow me to investigate this topic further and create my own sequence? Any books or other resources would also be appreciated.