The positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd and 10th positive integers, respectively, that have this property. We will call a positive number whose square ends in '44' as a "44-number".
If 'x' is the nth 44-number, we define the function 'S(n)' to be the sum of the digits of 'x^2' but excluding the ending '44'. So in the cases above, S(3) = 11 and S(10) = 17. We noticed that both of these sums are primes.We define 'P(n)' as the number of prime S(n)'s among the first 'n' 44-numbers. Write a function that returns P(n), given that P(3) = 2 and P(10) = 5.
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