How many numbers do have a digit sum of 23? How frequent is the digit sum 32?
Astonishingly, 6% of the numbers below 100000 have a digit sum of 23:
This seems pretty high, doesn’t it? It suggests that the digit sum is not evenly distributed, and it is, in fact, not:
As you see, the numbers 13 and 14 have the highest share as a digit sum of numbers below 1000. For values smaller than 10000, it is 18. And for values smaller than 100000, with 6% of all numbers, 22 and 23 are the most common digit sums.
If I’d had to start a conspiracy theory, I’d choose one of these. Also note how the gaussian distribution appeared out of nowhere.
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