In the infinite series: 1 + 3 + 3 + 3 + 5 + 5 + 5 + 5 + 5 + 7 + ... each positive odd integer k appears k times in consecutive order.

1) Write a general formula that can be used to find the n_th term of the series.

2) Prove that if n is not 3, then the n_th partial sum of the series is never prime.

By observation

k = 2 * Ceiling(sqrt(n)) - 1

Posted by Leming on 2007-01-08 12:20:18