A115765 Triangle read by rows: row n (n>=2) gives a set of n primes with the property that the averages of all subsets are all primes, having the smallest largest element.

3, 7, 5, 17, 29, 5, 509, 1013, 1109

Offset: 2

Author

T. D. Noe, Jan 30 2006

Keywords

• nonn
• tabf
• hard
• more

Comments

See A113833 for the case of all subset averages being distinct primes. The Mathematica program is for row 4.

Examples

			The set of primes generated by {5, 17, 29} is {5, 11, 17, 17, 17, 23, 29}.
Triangle begins:
3, 7
5, 17, 29
5, 509, 1013, 1109
		

Links

• Andrew Granville, Prime number patterns

Programs

Mathematica

Needs["DiscreteMath`Combinatorica`"]; nn=PrimePi[1277]; Do[s=Prime[{l, k, j, i}]; ss=Rest[Subsets[s]]; ave=(Plus@@@ss)/(Length/@ss); If[And@@(IntegerQ/@ave) && And@@PrimeQ[ave], Break[]], {l, 2, nn}, {k, 2, l-1}, {j, 2, k-1}, {i, 2, j-1}]; Reverse[s]