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A174721
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Integers z that cannot be largest number in the group of consecutive positive integers, sum of whom is average of twin prime pairs.
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0
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1, 2, 4, 10, 13, 20, 31, 33, 48, 55, 64, 66, 70, 82, 98, 103, 241, 280
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OFFSET
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1,2
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COMMENTS
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Consider a group of consecutive positive Integers : a+b+...+y+z = Average of twin prime pairs. Number 4:: 1+2+3+4=10, 2+3+4=9, 3+4=7. Total 3 possible combination; all 3 sums are Not averages of twin prime pairs; number 4 part of this sequence 1+2+3=6, 3+4+5=12 == averages of twin prime pairs, numbers 3 and 5 are Not in this sequence.
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LINKS
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MATHEMATICA
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mx=2500; mz=mx+(mx+1); lst={}; Do[p=a; Do[p+=n; If[PrimeQ[p-1]&&PrimeQ[p+1], AppendTo[lst, n]], {n, a+1, mx+1}], {a, 1, mx}]; z=Union@lst; Complement[Range[mx], z]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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