A Hundred Sequences Traced

The Prompt

Compute the Collatz sequence for every integer from 1 to 100 — by hand, by spreadsheet, or by a program you write yourself. For each, record the number of steps to reach 1 (the stopping time) and the maximum value attained (the peak). Identify the starting value with the longest stopping time and the one with the highest peak. Attend to the experience: at what point does the pattern feel predictable, and where does it surprise?

Completion Criteria

A table of stopping times and peaks for 1 through 100, the identification of the longest and highest trajectories, and a brief note on where predictability gave way to surprise.

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