// 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()));
}