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%I #3 Mar 31 2012 12:38:35
%S 1,2,4,10,13,20,31,33,48,55,64,66,70,82,98,103,241,280
%N Integers z that cannot be largest number in the group of consecutive positive integers, sum of whom is average of twin prime pairs.
%C 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.
%t 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]
%Y Cf. A014574, A174716, A174717
%K nonn
%O 1,2
%A _Vladimir Joseph Stephan Orlovsky_, Mar 28 2010
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