Put A Number Collatz Interactive Calculator

What is the Collatz Conjecture?

The Collatz Conjecture, proposed by Lothar Collatz in 1937, is a simple arithmetic statement that has defied proof for over 80 years. The conjecture states:

Despite its simplicity, the conjecture remains unproven. Mathematicians have verified the sequence for many numbers, but no general proof exists that it always reaches 1 for any starting value.

The sequence generated by the Collatz Conjecture is often called the "Hailstone sequence" because the numbers can grow and shrink unpredictably, like hailstones in a storm.

How to Use This Calculator

Using the interactive calculator is simple:

1. Enter any positive integer in the input field
2. Click "Calculate" to generate the sequence
3. View the complete sequence in the results panel
4. See a visualization of the sequence in the chart
5. Click "Reset" to start over

Formula Used

The calculator implements the following recursive formula:

The sequence is generated by repeatedly applying this function to the current value until it reaches 1 or reaches the maximum step limit.

Worked Examples

Example 1: Starting with 6

6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1

This sequence reaches 1 in 8 steps.

Example 2: Starting with 19

19 → 58 → 29 → 88 → 44 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

This sequence reaches 1 in 20 steps.

Example 3: Starting with 27

27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → 161 → 484 → 242 → 121 → 364 → 182 → 91 → 274 → 137 → 412 → 206 → 103 → 310 → 155 → 466 → 233 → 700 → 350 → 175 → 526 → 263 → 790 → 395 → 1186 → 593 → 1780 → 890 → 445 → 1336 → 668 → 334 → 167 → 502 → 251 → 754 → 377 → 1132 → 566 → 283 → 850 → 425 → 1276 → 638 → 319 → 958 → 479 → 1438 → 719 → 2158 → 1079 → 3238 → 1619 → 4858 → 2429 → 7288 → 3644 → 1822 → 911 → 2734 → 1367 → 4102 → 2051 → 6154 → 3077 → 9232 → 4616 → 2308 → 1154 → 577 → 1732 → 866 → 433 → 1300 → 650 → 325 → 976 → 488 → 244 → 122 → 61 → 184 → 92 → 46 → 23 → 70 → 35 → 106 → 53 → 160 → 80 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

This sequence reaches 1 in 111 steps.