"Additive Prime" Lab
- From the compendium of Mr. Merlis' exciting math/programming puzzles.

An "additive prime" can be defined to be a number within a set such that it can not be formed by summing any two or more other numbers in the set.

The set begins: {1, 2,...}

3 would not be in the set because 1 + 2 = 3

The set continues {1, 2, 4, ...}

Note that 5, 6, 7 can not be part of the set because they can be formed by adding two or more of the elements that precede it.

YOUR TASK: Determine the largest list of "additive primes" from 1-n. Your answer should be the number of elements.

A programming perspective: You can create a program to do this using a loop (or two?) that populates an ArrayList. The issue, of course, is determining if a formula exists to calculate the number of elements in a list of size n.