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In ideal world, I would prefer coins to be powers of 2.

It requires 7 coins in [ 1 .. 64 ] range to reach 100, but the average of popcnt( 1 .. 99 ) is only 3.19 coins per transaction, way better than 4.1 coins.

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Now account for the amount of mental overhead required for the average person to calculate change or coinage of a random amount in base two coins, as opposed to multiples of 5 or 10, and see if your 3.19 coins per transaction really saves you time.

One could simply switch to a base 16 numbering system as well!

I think the amount of mental overhead with base 2 coins is still less than with the proposed [ 1, 3, 11, 37 ] solution.

Great idea! Let's also make them double in diameter and density each denomination increase.

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