For a paper, I need to answer to problems pertaining to the averages of numbers. For example, how many prime numbers are the averages of other prime numbers, how many perfect squares/Fibonacci ect. I have found patterns for the above that demonstrate the existence of infinite number of pairs that work, but there is one that has stumped me. It is "how many terms in the sequence 1, 3, 6, 10, 15, ... can be written as the average of other terms of the sequence?" I have only been able to find a few valid pairs of terms with no pattern (that would show infinite numbers of pairs) in sight. I have also determined that the formula is (x^2-x)/2, but that's it. I would really appreciate any help on this.
Averages of numbers problem.
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