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On Conway's Generalization Of The 3x + 1 Problem, Robin M. Givens

Honors Theses

This thesis considers a variation of the 3x+1, or Collatz, Problem involving a function we call the Conway function. The Conway function is defined by letting C3(n)=2k for n=3k and C3(n)=4k±1 for n=3k±1, where n is an integer. The iterates of this function generate a few 'short' cycles, but the s' tructural dynamics are otherwise unknown. We investigate properties of the Conway function and other related functions. We also discuss the possibility of using the Conway function to generate keys for cryptographic use based on a fast, efficient binary implemenation of the function. Questions related to the conjectured tree-like structure …