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For each positive digit D and positive integer k, we use the symbol D(k) to represent the positive integer having exactly k digits, each of

  1. For each positive digit D and positive integer k, we use the symbol D(k) to represent

    the positive integer having exactly k digits, each of which is equal to D. For example,

    2(1) = 2 and 3(4) = 3333. There are N quadruples (P,Q,R,k) with P, Q and R 2

    positive digits, k a positive integer with k 2018, and P(2k) Q(k) = R(k) . The sum of the digits of N is

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