I had a headslap moment right after posting, my apologies.

Why should testing f(8) return 4 instead of 2?

I'm sorry, for clarity, are my equations the problem? They are not a solution that worked for me, simply an approach I tried before finding one that did. However, if that is the issue I will mark it.

Thanks for letting me know.

Thank you again for taking the time to share these resources with me, I am finishing my BaS in Secure Software Development, and the focus on security methodologies, development lifecycles, and all the fun stuff associated with that path has me polishing my own discrete mathmatics skills and I'm working through the open MIT pre-req's right now. I'm always amazed at how interesting math is when approached correctly versus the embarrasment that was my primary school days.

Best of luck and I hope I see you around the boards.

Fantastic explanation!

Thank you for taking the time to explain that as well as to introduce me to the concept of attractors, I actually tried a multithreaded approach with itterative equations that was less elegant, attractors is the perfect solution to the issues I was having there. My equations looked like the this.

        special_five = (-2 * special_five ** 3 + 3 * special_five ** 2) % (10 ** (k + 1))
        special_six = 10 ** (k + 1) + 1 - special_five

I like the quality of the comments, It helps demonstrate the multiple approaches that are possible. I attempted a multithreaded solution similair in the beginning and ran into issues with the limits of string length and int conversion.

This bit here,

GREEN |= {f, p-f+1}

Would you mind helping me wrap my brain around it?