Currency denominations (coins and bills) are usually based on numbers like 1, 2, 5, 10, 25, 50, 100, 200, etc.<p>An extreme example is that Japanese yen are denominated as 1, 5, 10, 50, 100, 500, 1000, 2000(uncommon), 5000, 10000. But I noticed that it takes a lot of 1's to pay or make change, whereas the 5's are less used.<p>What if we use denominations like 1 and 3 instead? The benefit is that the ratio 1:3 is similar to the ratio 3:10, so they are more evenly spaced on a logarithmic scale. Specifically, I'd like to explore what happens if the denominations are 1, 3, 10, 30, 100, 300, 1000, 3000, etc...