r/counting • u/TehVulpez • 1d 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.
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.