Halve it if even, triple-plus-one if odd

Start with any positive integer. If it is even, halve it; if odd, multiply by three and add one. The conjecture: no matter what number you start with, the sequence eventually reaches 1. Verified by computer for every number up to 2⁶⁸, never proven. Mapped backwards from 1, the chain of all integers forms a coral-like tree.

Seed n

slider: 1 … 10 000 · input: 1 … 1,000,000

Stats

Steps: 111
Peak value: 9,232
Peak step: 77
Path length: 112

Show inverse tree

Tree depth8

Backwards from 1: each v has parent 2v (always) and (v−1)/3 if v ≡ 4 mod 6 and the result is odd > 1. Capped at 280 nodes; the current seed's orbit glows cyan when it hits the tree.

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Hailstone trajectory · n = 27

n → n/2 or 3n + 1

Starting n

Steps to 1

111

Peak value

9,232

Peak at step

Inverse coral · backwards tree rooted at 1 · depth 8 · 17 nodes

The Collatz Conjecture