Fooling around with the Collatz Sequence

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 thoughts on “Fooling around with the Collatz Sequence

    1. 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.

    2. 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

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