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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. 0
 2, 7, 67, 1277, 2484733 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Andrew Granville, Prime number patterns EXAMPLE For any set of n elements, there are 2^n - 1 nonempty subsets. For n=3, consider the set {7, 19, 67}. The averages of the 2^3 - 1 = 7 nonempty subsets are:   avg({7}) = 7   avg({19}) = 19   avg({67}) =  67   avg({7, 19}) = 13   avg({7, 67}) = 37   avg({19, 67}) = 43   avg({7, 19, 67}) = 31 All these averages are different primes, and no such set exists with the largest element < 67. Hence, a(3) = 67. Sets which minimize the largest elements are: n = 1 {2} n = 2 {3, 7} n = 3 {7, 19, 67} n = 4 {5, 17, 89, 1277} n = 5 {209173, 322573, 536773, 1217893, 2484733} CROSSREFS For n > 1, largest element of row n of A113833. Sequence in context: A133237 A099660 A207978 * A225156 A260968 A322223 Adjacent sequences:  A307243 A307244 A307245 * A307247 A307248 A307249 KEYWORD nonn,hard,more AUTHOR Bert Dobbelaere, Mar 30 2019 STATUS approved

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Last modified April 3 19:43 EDT 2020. Contains 333198 sequences. (Running on oeis4.)