How this calculator works
For the standard rules, divide an even term by two and replace an odd term by three times itself plus one. Count each replacement as one transition, stopping at the first 1. Exact integer arithmetic avoids rounding large terms. A finite trace only checks the chosen start; it does not prove the conjecture for all positive integers. Custom rules can repeat or grow, so the trace has a limit.
Formula
Standard recurrence: aₖ₊₁ = aₖ/2 for even aₖ; aₖ₊₁ = 3aₖ + 1 for odd aₖ. This page reports the total stopping time to 1 when reached.
Worked example
Starting at 6 gives 6, 3, 10, 5, 16, 8, 4, 2, 1. There are eight transitions and the maximum is 16. Starting at 3 reaches 1 after seven transitions.
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Frequently asked questions
Is the starting value counted as a step?
It is row zero. The step count records transitions, so starting at 1 gives zero.
What if the step limit is reached?
The page reports the partial trace and says that the limit was reached. It does not infer divergence.
How are custom even rules restricted?
The multiplier must be a non-negative multiple of one half. This keeps every even integer integral. All resulting terms must remain positive.