Puzzle/sequence/programming exercise inspired by vague question on Mathpuzzle site. Given k, what is the fewest number of terms needed to get the best possible approximation to pi (or e) as a sum of (positive) fractions with denominators <= k? For example, if k = 8, the closest you can come to pi is 377/120 (Fib/Fac!), and this can be done with at best three terms (2/3 + 3/5 + 15/8).