1-2-4-8-… is good because regular: The divisors are always 2.
1-2-5 is “better” because: a) Just like normal money. Familiar to humans. Tech minds often forget how important. b) Close to regular: The divisors are almost always 2, except third of cases when it’s 1/8th bigger: 2, 2.5, 2, and repeat.
However. Maybe you are right. It’s already not 100% regular. But it’s regularly irregular. Similar could be implemented to tweak exponent for the “total value of coins in this denomination” series which is the 4th column on the picture. That column / coin denomination = number of coins in the denomination.
However. Tweaking is not so simple as you say. Like “4:8:5”. No:
First: Need to know distribution of transaction amounts. Log-Normal maybe good first approximation. Take Log-Mean as 0: It changes when Safe Coin price changes. So: Any number is good. Log-Variance: Take it from real transaction amounts. I don’t know where to get this data.
Then: Needs simulation to determine best locally irregular composition of coin denominations to represent division of market cap distributed as determined in first step. (Sorry. Complicated sentence. Took me time.)
“Locally irregular tweaking”: 3 steps, almost the same, juts little different. But every 3rd step is the same. I have this for denomination step: 2, 2.5, 2, 2, 2.5, 2, 2, 2.5, 2… For “series value” it’s about 1.468466, repeating. Tweaked, it could be: 1.468466 * a, 1.468466, 1.468466 / a, 1.468466 * a, 1.468466, 1.468466 / a, 1.468466 * a, 1.468466, 1.468466 / a… Globally, it’s 1.468466. But locally irregular.