Collatz Conjecture Calculator – 3n+1 Steps

The Collatz process applies one of two rules forever: halve even numbers, triple-and-add-one to odd numbers. Every starting value ever tested eventually reaches 1, but nobody has proved this for all integers — the Collatz conjecture, open since 1937. Starting at 6: even, so 3; odd, so 10; then 5, 16, 8, 4, 2, 1 — eight steps, peak value 16. Starting at 27 the ride is wild: 111 steps and a maximum of 9,232 before collapsing to 1. The calculator lists every hop, the step count, the peak value, and a mini-chart of the trajectory. Total stopping times vary irregularly: 15 takes 17 steps, 16 only 4 (straight halving), and 41 takes 65. Entering 1 shows the terminal cycle 1 → 4 → 2 → 1, which the tool halts at by convention.

1. 1

   Enter a starting number

   Any positive integer, e.g. 6 or 27

2. 2

   Apply the parity rule

   Even → n/2; odd → 3n+1, with each hop printed

3. 3

   Track steps and peak

   Count of steps and maximum value are reported

4. 4

   Reach 1 and stop

   The sequence halts at the 4-2-1 cycle

• 1

  Powers of 2 fall straight down: 16 → 8 → 4 → 2 → 1

• 2

  27 is the classic long flight: 111 steps, peak 9,232

• 3

  The conjecture remains unproven for all integers

• Applying 3n+1 to even numbers — parity check comes first

• Counting the starting number as a step

• Forgetting the process only promises behavior for positive integers

• Expecting stopping time to grow with n — 27 outruns many larger starts