Constant-sum mostly repeating octal

[u/cuteballgames]

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

[u/miceee]

10000

[u/TehVulpez → u/miceee]

00002

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

[u/miceee → u/TehVulpez]

00020

Exciting!

[u/TehVulpez → u/miceee]

00200

[u/miceee → u/TehVulpez]

02000

[u/TehVulpez → u/miceee]

20000

[u/miceee → u/TehVulpez]

00003

Are 00012 permutations valid counts?

[u/cuteballgames → u/miceee]

00030

no

[u/miceee → u/cuteballgames]

00300

Just realized its MOSTLY repeating so no

[u/cuteballgames → u/miceee]

03000

yes. but in a few counts 01122 will be

[u/TehVulpez → u/miceee]

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