Collatz (3n+1) Sequence
The famous unproven conjecture, plotted out.
Sequence (112 terms)
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
The Collatz conjecture (also called 3n+1): start with any positive integer. If it's even, halve it. If it's odd, triple it and add 1. The conjecture says you always reach 1, no matter where you start. It's been verified for n up to 2^68 but never proven. Try 27 for fun: it climbs above 9000 before settling.
About
Enter any positive integer. The tool runs the Collatz process: halve if even, triple-and-add-one if odd. Repeat. Get the full sequence, peak value, and number of steps to reach 1. Tries 5,000 steps before giving up.
How to use
- Enter a starting integer.
- Read the sequence.
FAQ
Has this conjecture been proven?+
No. It's been verified by computer for n up to 2^68 (≈ 295 quintillion) but never proven. Paul Erdős reportedly said "mathematics may not be ready for such problems."
Why is 27 famous?+
Starting from 27, the sequence climbs to 9,232 before settling. 111 steps to 1. It's the smallest n that takes more than 100 steps.