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A317680

Least sum S_n of n distinct primes p_i such that q_j = n*p_j - Sum_{k=1..n,k!=j} p_k, j=1..n is prime, such that the set union {p_i} U {q_i} contains 2*n distinct primes.

The sets of primes p_i and q_i and a description of the problem are provided in A317678 and A317679. a(1) is omitted to indicate the nonexistence of a solution.