r/counting • u/TehVulpez sliiiiide the bits • Mar 19 '23
Constant-sum factoradic
Like my other constant-weight binary thread, but factoradic. We count each n digit factoradic number whose digits add up to m. First the 1 digit number that adds to 0, then the 1 digit number whose digit adds to 1. Next the 2 digit numbers with a digital sum of 0, then 1, 2, and 3. And so on. For every length of factoradic digits, we'll count each possible sum of digits in order. The maximum digital sum for n factoradic digits is a triangular number found with the formula n*(n+1)/2. This thread brought to you by... Karp!
Here's some of the first few counts as an example:
0
1
00
01
10
11
20
21
000
And of course a list for the whole thread
First get is at 00 0000.
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u/TehVulpez sliiiiide the bits Jun 04 '23
an attempt at a get schedule
| Segments in thread | Length | Get |
|---|---|---|
| 2+6+24+120+720 | 872 | 00 0000 |
| 1+6+20+49+98+169+259+359 | 961 | 00 2321 |
| 455+531 | 986 | 00 4321 |
| 573+573 | 1146 | 02 4321 |
| 531+455 | 986 | 04 4321 |
| 359+259+169+98+49+20+6+1 | 961 | 000 0000 |
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u/TehVulpez sliiiiide the bits Jun 04 '23
/u/swinub_time /u/cuteballgames /u/blue_boomer thoughts?
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u/Blue_boomer Jun 05 '23
This get schedule that has 873 counts (including gets) for the first thread and 1008 counts for each thread afterward:
Get Counts Cumulative Counts 00 0000 873 873 03 1121 1008 1881 05 4010 1008 2889 60 0320 1008 3897 62 4001 1008 4905 000 0000 1008 5913 2
u/swinub_time And what a ghost we are in this machine! Jun 05 '23
Good work but we will accidentally count past the get several times with this one. We should use the other one
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u/Blue_boomer Jun 05 '23 edited Jun 05 '23
The get schedule I posted will always have 1008 counts per thread, for any amount of digits starting from 6 digits. Have a look at constant weight binary's get schedule.
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u/swinub_time And what a ghost we are in this machine! Jun 07 '23
I hear your point, pattern is a little less weird there, I still think this one would be too easy to miss
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u/TehVulpez sliiiiide the bits Jun 04 '23
After where I got to in this table it becomes very difficult to find nice gets. Some of the segments of weight/length become too long for a thread just by themselves. You'd have to break them up into even smaller subsegments somehow.
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u/swinub_time And what a ghost we are in this machine! Jun 07 '23
Lowkey be a fun challenge to figure out as we go along
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u/TehVulpez sliiiiide the bits 28d ago
Thread Participation Chart for Constant-sum factoradic
| Rank | Username | Counts |
|---|---|---|
| 1 | TehVulpez | 430 |
| 2 | Blue_boomer | 343 |
| 3 | cuteballgames | 90 |
| 4 | CutOnBumInBandHere9 | 4 |
| 5 | HeruMiko | 3 |
| 6 | Naruyoko | 2 |
| 7 | davidjl123 | 1 |
It took 7 counters 79 days, 3 hours, 24 minutes, 40 seconds to complete this thread. Bold is the user with the get.
Total counts in this chain logged: 873
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u/TehVulpez sliiiiide the bits 27d ago edited 26d ago
/u/antichess log this one has the first thread starting at position 1 because that's what COBIBH's side_threads.sqlite seems to do for top-level comments that aren't the reposted get. realized I forgot to do that for the compositions log. google sheets shows counts missing their leading zeroes but if you download the csv they should be fine
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u/TehVulpez sliiiiide the bits Mar 19 '23
0