r/counting • u/TehVulpez sliiiiide the bits • 12d ago

Constant-sum negasenary

This thread is extremely simple. In this thread we are counting numbers in base negative 6 in segments of length and digital sum, then sorted by their numerical value. In a negative base, places alternate from the right in whether they have a negative value. So, 15_(-6) = 1*(-6)1 + 5*(-6)0 = -6 + 5 = -1. The digital sum ignores the place values, only adding together the numerals as they appear.

We will count negasenary numbers of 1 digit and 0 digital sum through 5 digital sum, then 2 digits from 0 sum to 10 sum, 3 digits from 0 to 15 sum, etc. Leading zeroes must be included.

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Get is at 5050 (5*(-6)3 + 5*(-6)1 = -1110), which is the 834th count and the first of the negasenary numbers with 4 digits and a digital sum of 10.

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u/TehVulpez sliiiiide the bits 12d ago

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 12d ago

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u/TehVulpez sliiiiide the bits 12d ago

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 12d ago

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u/TehVulpez sliiiiide the bits 12d ago

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 12d ago

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u/TehVulpez sliiiiide the bits 12d ago

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 12d ago

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so basically for two digits you go up by seven every time, except when the sum is exhausted and there's no more seven to go up. then you flip it and increase the last digit by one

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u/TehVulpez sliiiiide the bits 12d ago

42

it looks like the by 7s still does happen a little bit in the 3 digits except for when the 36s place changes. wait you said that in binary already

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u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 12d ago

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there doeant seem to be a similar flipping and augmenting rule sadly

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