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

2,1

Comments

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

Links

Table of n, a(n) for n=2..10.

Andrew Granville, Prime number patterns

Example

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

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]

Crossrefs

Sequence in context: A345401 A059912 A354008 * A282598 A269369 A305421

Adjacent sequences: A115762 A115763 A115764 * A115766 A115767 A115768

Keyword

nonn,tabf,hard,more

Author

T. D. Noe, Jan 30 2006

Status

approved