๐ŸŒ€ Collatz Sequence Visualizer

111Steps
9,232Peak value
Sequence
27 โ†’ 82 โ†’ 41 โ†’ 124 โ†’ 62 โ†’ 31 โ†’ 94 โ†’ 47 โ†’ 142 โ†’ 71 โ†’ 214 โ†’ 107 โ†’ 322 โ†’ 161 โ†’ 484 โ†’ 242 โ†’ 121 โ†’ 364 โ†’ 182 โ†’ 91 โ†’ 274 โ†’ 137 โ†’ 412 โ†’ 206 โ†’ 103 โ†’ 310 โ†’ 155 โ†’ 466 โ†’ 233 โ†’ 700 โ†’ 350 โ†’ 175 โ†’ 526 โ†’ 263 โ†’ 790 โ†’ 395 โ†’ 1186 โ†’ 593 โ†’ 1780 โ†’ 890 โ†’ 445 โ†’ 1336 โ†’ 668 โ†’ 334 โ†’ 167 โ†’ 502 โ†’ 251 โ†’ 754 โ†’ 377 โ†’ 1132 โ†’ 566 โ†’ 283 โ†’ 850 โ†’ 425 โ†’ 1276 โ†’ 638 โ†’ 319 โ†’ 958 โ†’ 479 โ†’ 1438 โ†’ 719 โ†’ 2158 โ†’ 1079 โ†’ 3238 โ†’ 1619 โ†’ 4858 โ†’ 2429 โ†’ 7288 โ†’ 3644 โ†’ 1822 โ†’ 911 โ†’ 2734 โ†’ 1367 โ†’ 4102 โ†’ 2051 โ†’ 6154 โ†’ 3077 โ†’ 9232 โ†’ 4616 โ†’ 2308 โ†’ 1154 โ†’ 577 โ†’ 1732 โ†’ 866 โ†’ 433 โ†’ 1300 โ†’ 650 โ†’ 325 โ†’ 976 โ†’ 488 โ†’ 244 โ†’ 122 โ†’ 61 โ†’ 184 โ†’ 92 โ†’ 46 โ†’ 23 โ†’ 70 โ†’ 35 โ†’ 106 โ†’ 53 โ†’ 160 โ†’ 80 โ†’ 40 โ†’ 20 โ†’ 10 โ†’ 5 โ†’ 16 โ†’ 8 โ†’ 4 โ†’ 2 โ†’ 1

Starting from any positive integer, repeatedly applies the rule "if even, divide by 2; if odd, multiply by 3 and add 1" until reaching 1 โ€” the Collatz conjecture (the 3n+1 problem) โ€” and charts how the value moves over time. It's famous as an unsolved conjecture: every starting positive integer is believed to eventually reach 1, though this has never been proven for all integers.

How to use

  1. Enter a starting positive integer.
  2. The sequence down to 1 is computed automatically, along with the step count and peak value reached.
  3. The chart shows how the value swings up and down along the way.

FAQ

What is the Collatz conjecture?

It's an unsolved conjecture in mathematics that repeatedly applying "if even, halve it; if odd, triple it and add 1" to any positive integer will always eventually reach 1. It's named after mathematician Lothar Collatz.

Has this been proven for all numbers?

Computer verification has confirmed it up to enormous starting values, but it has never been proven for all positive integers โ€” it remains an open problem in mathematics.

What happens starting from 27?

27 is a famous example of a surprisingly long sequence for such a small starting number โ€” it takes 111 steps and peaks at 9232 along the way.

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