Collatz Meets Möbius
Take a number k. Count the steps S(k) it requires to reach 1 under the Collatz process. Apply the Möbius function μ to that step count. Sum the result from k = 1 to m. The partial sums do not wander. They repeat, including the fine jagged structure of individual peaks. Not approximately. Exactly.
The Möbius function μ(n) returns one of three values: 0 if…
