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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

Table of n, a(n) for n=1..5.

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.)