1, 2, 4, 6, 12, 14, 60...

Why is there only o e odd member?

These are the numbers n such that the sum of the first n primes is prime (OEIS A013916). The first 1 prime is of course prime. After that first prime all the rest of the primes are odd. Since the first prime, 2, is even, an even number of added primes would make an even total, but an odd total is needed in order for that total to be prime. So the primes included in the total, beyond the prime 2, must be odd in number, but since the count of primes includes the first, the actual count, including the first, must be even.

Posted by Charlie on 2018-08-19 14:13:48