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

108, 570, 858, 1452, 3330, 6792, 7458, 9420, 9630, 10710, 10890, 13722, 17388, 18120, 25032, 27582, 27792, 34032, 68712, 68898, 72270, 76830, 78978, 81372, 89820, 90402, 95232, 99708, 104472, 119772, 122868, 125790, 138078, 165312

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Keywords

• nonn
• less

Examples

			Averages of twin prime pairs: 4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150, ...
108 = 6 + 12 + 18 + 30 + 42, 570 = 72 + 102 + 108 + 138 + 150, ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A040040, A014574, A160916, A160917, A160918

Programs

Mathematica

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
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 *)