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A307246 Smallest k for which a set of n primes <= k exists so that the averages of all nonempty subsets are all distinct primes.

%I A307246 #11 Apr 01 2019 08:34:39
%S A307246 2,7,67,1277,2484733
%N A307246 Smallest k for which a set of n primes <= k exists so that the averages of all nonempty subsets are all distinct primes.
%H A307246 Andrew Granville, <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimePatterns.pdf">Prime number patterns</a>
%e A307246 For any set of n elements, there are 2^n - 1 nonempty subsets.
%e A307246 For n=3, consider the set {7, 19, 67}.
%e A307246 The averages of the 2^3 - 1 = 7 nonempty subsets are:
%e A307246   avg({7}) = 7
%e A307246   avg({19}) = 19
%e A307246   avg({67}) =  67
%e A307246   avg({7, 19}) = 13
%e A307246   avg({7, 67}) = 37
%e A307246   avg({19, 67}) = 43
%e A307246   avg({7, 19, 67}) = 31
%e A307246 All these averages are different primes, and no such set exists with the largest element < 67. Hence, a(3) = 67.
%e A307246 Sets which minimize the largest elements are:
%e A307246 n = 1 {2}
%e A307246 n = 2 {3, 7}
%e A307246 n = 3 {7, 19, 67}
%e A307246 n = 4 {5, 17, 89, 1277}
%e A307246 n = 5 {209173, 322573, 536773, 1217893, 2484733}
%Y A307246 For n > 1, largest element of row n of A113833.
%K A307246 nonn,hard,more
%O A307246 1,1
%A A307246 _Bert Dobbelaere_, Mar 30 2019