cp's OEIS Frontend

The following is quoted (with minor changes) from Alan Burdick's article: "Jeffrey Shallit analyzed the average handful of change, and devised a clever way to reduce its size. Getting rid of the 1-cent coin, a plot advocated by numerous antipennyists, would certainly help, he says. But Shallit's own scheme for reducing loose change involves the creation of an entirely new coin. What the United States needs, he says, is an 18-cent piece. Shallit reached this conclusion by a linear Diophantine equation. Shallit calculated that the average U.S. transaction produces 4.7 coins in change. If we got rid of the dime and replaced it with an 18-cent coin, the 'cost' of the average transaction would drop from 4.7 to 3.89 coins. A system of coins worth 1¢, 5¢, 18¢, and 29¢ would have the same effect. Should we wish to keep the dime and simply add a fifth denomination, the best coin to add would be 32¢, for an efficiency of 3.46. Even better, if we kept the dime and actually used the half-dollar, then added an 18-cent coin to that mix, we'd gain maximum efficiency: You'd get back a mere 3.18 coins per transaction."

Nonnegative integers representable as a linear combination of 1, 5, 10, 25, and 50 with nonnegative coefficients, minimal sum of coefficients, and all nonzero coefficients equal.

Includes all nonnegative multiples of 50 and every term > 204 is a multiple of 50.

Unlike A212773, here it is permitted--and necessary--to use a single denomination for some amounts; otherwise, this sequence would be finite.

The European Union uses eight coins - worth 1, 2, 5, 10, 20, and 50 cents, plus 1- and 2-Euro coins - with a range of values from 0 to 499. The average cost of making change in Europe, Jeffrey Shallit calculates, is 4.6 coins. The best way to lower the cost, to 3.92, would be for Europeans to add yet another coin, worth either 1.33 or 1.37 Euros (the sequence as shown uses 133, though 137 is an equally valid solution).