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A115765
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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.
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0
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OFFSET
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2,1
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COMMENTS
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See A113833 for the case of all subset averages being distinct primes. The Mathematica program is for row 4.
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LINKS
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Table of n, a(n) for n=2..10.
Andrew Granville, Prime number patterns
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EXAMPLE
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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
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A090916 A184162 A059912 * A112071 A046561 A097406
Adjacent sequences: A115762 A115763 A115764 * A115766 A115767 A115768
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KEYWORD
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hard,nonn,tabl
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AUTHOR
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T. D. Noe, Jan 30 2006
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STATUS
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approved
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