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

1,1

Links

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

Example

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, ...

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 *)

Crossrefs

Cf. A040040, A014574, A160916, A160917, A160918

Sequence in context: A063880 A059436 A233685 * A129027 A288706 A204276

Adjacent sequences: A160916 A160917 A160918 * A160920 A160921 A160922

Keyword

nonn,less

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Status

approved