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

2, 7, 67, 1277, 2484733

Offset: 1

Author

Bert Dobbelaere, Mar 30 2019

Keywords

• nonn
• hard
• more

Examples

			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}
		

Links

• Andrew Granville, Prime number patterns

Crossrefs

For n > 1, largest element of row n of A113833.