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A160919 Averages of twin prime pairs that are sums of 5 consecutive averages of twin prime pairs.

%I A160919 #16 Sep 26 2024 12:45:43
%S A160919 108,570,858,1452,3330,6792,7458,9420,9630,10710,10890,13722,17388,
%T A160919 18120,25032,27582,27792,34032,68712,68898,72270,76830,78978,81372,
%U A160919 89820,90402,95232,99708,104472,119772,122868,125790,138078,165312
%N A160919 Averages of twin prime pairs that are sums of 5 consecutive averages of twin prime pairs.
%H A160919 Harvey P. Dale, <a href="/A160919/b160919.txt">Table of n, a(n) for n = 1..1000</a>
%e A160919 Averages of twin prime pairs: 4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150, ...
%e A160919 108 = 6 + 12 + 18 + 30 + 42, 570 = 72 + 102 + 108 + 138 + 150, ...
%t A160919 PrimeNextTwinAverage[n_]:=Module[{k},k=n+1; While[ !PrimeQ[k-1]||!PrimeQ[k+1],k++ ];k];lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],a=n;b=PrimeNextTwinAverage[a]; c=PrimeNextTwinAverage[b]; d=PrimeNextTwinAverage[c];e=PrimeNextTwinAverage[d]; a=a+b+c+d+e; If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,a]]],{n,3*8!}];lst
%t A160919 Select[Total/@(Partition[Mean/@Select[Partition[Prime[Range[10000]],2,1],#[[2]]-#[[1]]==2&],5,1]),AllTrue[#+{1,-1},PrimeQ]&] (* _Harvey P. Dale_, Sep 26 2024 *)
%Y A160919 Cf. A040040, A014574, A160916, A160917, A160918
%K A160919 nonn,less
%O A160919 1,1
%A A160919 _Vladimir Joseph Stephan Orlovsky_, May 30 2009