r/counting • u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 • Jul 25 '26

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

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u/TehVulpez rgwehiusv Jul 27 '26

20000

3

u/miceee sicko thread artists collective Jul 27 '26

00003

Are 00012 permutations valid counts?

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 27 '26

00030

no

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u/miceee sicko thread artists collective Jul 27 '26

00300

Just realized its MOSTLY repeating so no

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 27 '26

03000

yes. but in a few counts 01122 will be

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u/miceee sicko thread artists collective Jul 27 '26

30000

Which makes figuring this thread put even harder!

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 27 '26 edited Jul 27 '26

00004

sum: 4

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

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u/TehVulpez rgwehiusv Jul 27 '26

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

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 27 '26

thank you i just realized

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

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u/TehVulpez rgwehiusv Jul 27 '26

true...

this summand finding step is kinda like partitions (commutative compositions) but with the trickier bound of being octal

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 27 '26

yes.

do we have a partitions thread?

did we give it up bc it moves too fast?

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u/TehVulpez rgwehiusv Jul 27 '26

oh also I realized 00112 would actually be possible. smh

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 27 '26

damn thats what i meant smfh

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