Spent some time working on https://projecteuler.net/problem=14

It was fun, and I produced:

Crunching Collatz Sequence...go make some coffee Number 13 also has same number of terms as previous record New record of 18 iterations found for 14 Number 15 also has same number of terms as previous record New record of 21 iterations found for 18 Number 19 also has same number of terms as previous record New record of 24 iterations found for 25 New record of 112 iterations found for 27 New record of 113 iterations found for 54 Number 55 also has same number of terms as previous record New record of 116 iterations found for 73 New record of 119 iterations found for 97 New record of 122 iterations found for 129 New record of 125 iterations found for 171 New record of 128 iterations found for 231 Number 235 also has same number of terms as previous record New record of 131 iterations found for 313 New record of 144 iterations found for 327 New record of 145 iterations found for 649 Number 654 also has same number of terms as previous record Number 655 also has same number of terms as previous record Number 667 also has same number of terms as previous record New record of 171 iterations found for 703 New record of 179 iterations found for 871 New record of 182 iterations found for 1161 New record of 183 iterations found for 2223 Number 2322 also has same number of terms as previous record Number 2323 also has same number of terms as previous record New record of 209 iterations found for 2463 New record of 217 iterations found for 2919 New record of 238 iterations found for 3711 New record of 262 iterations found for 6171 New record of 268 iterations found for 10971 New record of 276 iterations found for 13255 New record of 279 iterations found for 17647 Number 17673 also has same number of terms as previous record New record of 282 iterations found for 23529 New record of 308 iterations found for 26623 New record of 311 iterations found for 34239 Number 35497 also has same number of terms as previous record New record of 324 iterations found for 35655 New record of 340 iterations found for 52527 New record of 351 iterations found for 77031 New record of 354 iterations found for 106239 New record of 375 iterations found for 142587 New record of 383 iterations found for 156159 New record of 386 iterations found for 216367 New record of 443 iterations found for 230631 New record of 449 iterations found for 410011 New record of 470 iterations found for 511935 New record of 509 iterations found for 626331 New record of 525 iterations found for 837799 The record number of terms was 525, Produced by number 837799

RUN FINISHED; exit value 0; real time: 320ms; user: 0ms; system: 300ms

### This felt good, so I bumped the target number up to 1 billion and got

Crunching Collatz Sequence...go make some coffee Number 13 also has same number of terms as previous record New record of 18 iterations found for 14 Number 15 also has same number of terms as previous record New record of 21 iterations found for 18 Number 19 also has same number of terms as previous record New record of 24 iterations found for 25 New record of 112 iterations found for 27 New record of 113 iterations found for 54 Number 55 also has same number of terms as previous record New record of 116 iterations found for 73 New record of 119 iterations found for 97 New record of 122 iterations found for 129 New record of 125 iterations found for 171 New record of 128 iterations found for 231 Number 235 also has same number of terms as previous record New record of 131 iterations found for 313 New record of 144 iterations found for 327 New record of 145 iterations found for 649 Number 654 also has same number of terms as previous record Number 655 also has same number of terms as previous record Number 667 also has same number of terms as previous record New record of 171 iterations found for 703 New record of 179 iterations found for 871 New record of 182 iterations found for 1161 New record of 183 iterations found for 2223 Number 2322 also has same number of terms as previous record Number 2323 also has same number of terms as previous record New record of 209 iterations found for 2463 New record of 217 iterations found for 2919 New record of 238 iterations found for 3711 New record of 262 iterations found for 6171 New record of 268 iterations found for 10971 New record of 276 iterations found for 13255 New record of 279 iterations found for 17647 Number 17673 also has same number of terms as previous record New record of 282 iterations found for 23529 New record of 308 iterations found for 26623 New record of 311 iterations found for 34239 Number 35497 also has same number of terms as previous record New record of 324 iterations found for 35655 New record of 340 iterations found for 52527 New record of 351 iterations found for 77031 New record of 354 iterations found for 106239 New record of 375 iterations found for 142587 New record of 383 iterations found for 156159 New record of 386 iterations found for 216367 New record of 443 iterations found for 230631 New record of 449 iterations found for 410011 New record of 470 iterations found for 511935 New record of 509 iterations found for 626331 New record of 525 iterations found for 837799 New record of 528 iterations found for 1117065 Number 1126015 also has same number of terms as previous record New record of 531 iterations found for 1501353 Number 1564063 also has same number of terms as previous record New record of 557 iterations found for 1723519 New record of 560 iterations found for 2298025 New record of 563 iterations found for 3064033 New record of 584 iterations found for 3542887 New record of 597 iterations found for 3732423 New record of 613 iterations found for 5649499 New record of 665 iterations found for 6649279 New record of 686 iterations found for 8400511 New record of 689 iterations found for 11200681 New record of 692 iterations found for 14934241 New record of 705 iterations found for 15733191 New record of 706 iterations found for 31466382 Number 31466383 also has same number of terms as previous record New record of 745 iterations found for 36791535 New record of 950 iterations found for 63728127 New record of 951 iterations found for 127456254 Number 127456255 also has same number of terms as previous record New record of 954 iterations found for 169941673 New record of 957 iterations found for 226588897 New record of 965 iterations found for 268549803 New record of 966 iterations found for 537099606 Number 537099607 also has same number of terms as previous record New record of 987 iterations found for 670617279 The record number of terms was 987, Produced by number 670617279 RUN FINISHED; exit value 0; real time: 7m 6s; user: 760ms; system: 7m 4s

This was single-core on a Virtual machine running on a core i5 (sandybridge).

I am not sure I want to test what 4 billion looks like without finding a way to use more than one thread.

I don’t think the answer is wrong, but I might have made a mistake I don’t yet realize 🙂

## 3 responses to “Fooling around with the Collatz Sequence”

There is currently a prize of US$2,500 plus a bottle of champagne for a valid solution to this problem (or a counter-example). See

http://unsolvedproblems.org/

Hi Tim,

Thanks for comment, and sorry for being so late to moderating it (real life :)).

I feel like my solution is correct, and this was a rather easy problem to solve, so I don’t think it is unsolved — however, I probably lack the mathematical skill to prove my solution. I can publish my code though, once I get back in front of my home computer.

Yea, well, my code doesn’t really prove it, it’s just a program that progressively tests and finds that the conjecture is true, up to 1 billion in my case… Proof by induction :p