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 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. 0
 3, 7, 5, 17, 29, 5, 509, 1013, 1109 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS See A113833 for the case of all subset averages being distinct primes. The Mathematica program is for row 4. LINKS 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: A090916 A184162 A059912 * A112071 A046561 A097406 Adjacent sequences:  A115762 A115763 A115764 * A115766 A115767 A115768 KEYWORD hard,nonn,tabl AUTHOR T. D. Noe, Jan 30 2006 STATUS approved

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Last modified May 18 07:10 EDT 2013. Contains 225419 sequences.