Computational and Mathematical Analysis of a Convergent Alphanumeric Reduction Algorithm

Consider the algorithm CARA: take a number, count the number of letters in its spelling to get a new number, and repeat. For example,

15 (fifteen) → 7 (seven) → 5 (five) → 4 (four) → 4 (four) → ···

We show that all such sequences end in the number 4.