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 A174721 Integers z that cannot be largest number in the group of consecutive positive integers, sum of whom is average of twin prime pairs. 0
 1, 2, 4, 10, 13, 20, 31, 33, 48, 55, 64, 66, 70, 82, 98, 103, 241, 280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS MATHEMATICA 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] CROSSREFS Cf. A014574, A174716, A174717 Sequence in context: A180427 A127591 A100912 * A026224 A034233 A056718 Adjacent sequences:  A174718 A174719 A174720 * A174722 A174723 A174724 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Mar 28 2010 STATUS approved

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)