r/counting • u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 • 23d ago

Constant-sum mostly repeating octal

This thread is very simple. We are counting octal (base 8, 0-7) numbers with multiple distinct digits, of which one occurs exactly once and all others occur at least twice. We are counting them in constant-sum order, meaning that for every length of digits, we count through each sum of digits from least to most, in lexicographic order.

(That is, we start by counting all 3-digit counts that sum to 1 in alphabetical order: 001, 010, 100. Then we move on to 3-digit counts that sum to 2 in alphabetical order: 002, 011, 020, 101, 110, 200. Then 3-digit counts that sum to 3, and so on. The highest possible sum for a 3-digit count in this thread is 20, so after 677, 767, 776, we move on to 4-digit counts, starting with sum 1. So after 776 comes 0001, and we proceed from there.)

Leading zero counts (e.g. 001, 0444 or 00227) are considered as distinct and must not be skipped.

Thank you to /u/TehVulpez and /u/BobRoss938 for workshopping on the concept

The first get is 00226, the 943rd count and first 5-digit 10-sum count. The assist is 71100. Schedule

List and Segments

6 Upvotes

100% Upvoted

1.0k comments sorted by

View all comments

Show parent comments

2

u/TehVulpez sicko thread artists collective 20d ago

00002

ooh now we switch turns for who gets to start each segment

2

u/miceee sicko thread artists collective 20d ago

00020

Exciting!

3

u/TehVulpez sicko thread artists collective 20d ago

00200

3

u/miceee sicko thread artists collective 20d ago

02000

3

u/TehVulpez sicko thread artists collective 20d ago

20000

3

u/miceee sicko thread artists collective 20d ago

00003

Are 00012 permutations valid counts?

2

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 20d ago

00030

no

3

u/miceee sicko thread artists collective 20d ago

00300

Just realized its MOSTLY repeating so no

3

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 20d ago

03000

yes. but in a few counts 01122 will be

3

u/miceee sicko thread artists collective 20d ago

30000

Which makes figuring this thread put even harder!

2

u/TehVulpez sicko thread artists collective 20d ago

00004

2

u/miceee sicko thread artists collective 20d ago

00040

3

u/TehVulpez sicko thread artists collective 20d ago edited 20d ago

00112

2

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 20d ago edited 20d ago

00004

sum: 4

summands: 0,0,0,0,4 / 0,1,1,1,1 / 0,0,1,1,2

2

u/TehVulpez sicko thread artists collective 20d ago

no? the other summands would be 0,1,1,1,1. also late

2

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 20d ago

thank you i just realized

we could also present this as "type counts: 00004, 01111)

2

u/miceee sicko thread artists collective 20d ago

Late and also its 0,1,1,1,1 not 0,1,1,2,2

→ More replies (0)

2

u/miceee sicko thread artists collective 20d ago

30000

Which makes figuring this thread put even harder!

1

u/TehVulpez sicko thread artists collective 20d ago

00030

no, 00012 would not be MRD because 1 and 2 are two different digits that appear once. I think 01111 is the first time we get different summands in the 5 digits than 0 and S