// Q65: Find the sum of digits in the numerator of the 100th // convergent of the continued fraction for e. public static int Q74() { // e = [2; 1,2,1, 1,4,1, 1,6,1 , ... , 1,2k,1, ...]. var quotients = Enumerable.Range(1, 33). SelectMany(i => new [] {1, i * 2, 1}). ToList(); quotients.Insert(0, 2); var numerators = new BigInteger[100]; Func<int, int, BigInteger> getNumerator = (idx, q) => { if (idx == 0) return 2; if (idx == 1) return 3; return (q*numerators[idx - 1]) + numerators[idx - 2]; }; for (int i = 0; i < numerators.Length; i++) { numerators[i] = getNumerator(i, quotients[i]); } return numerators.Last().ToString().Sum(c => Int32.Parse(c.ToString())); }