A160916 Averages of twin prime pairs which are a sum of averages of two consecutive twin prime pairs.

18, 30, 72, 102, 660, 1092, 1302, 2082, 2112, 2382, 2592, 2970, 4242, 4272, 4650, 4722, 4932, 5442, 5520, 6690, 6762, 7590, 8220, 9000, 10332, 10860, 11160, 11718, 11970, 13002, 16452, 17658, 18522, 20232, 22278, 23040, 23910, 24180, 24918

Offset

1,1

Comments

Values A014574(j) of the form A014574(k) + A014574(k+1).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

18=A014574(4) is in the sequence because it equals A014574(2)+A014574(3) = 6+12.
30=A014574(5) is in the sequence because it equals A014574(3)+A014574(4) = 12+18.
72=A014574(8) is in the sequence because it equals A014574(5)+A014574(6) = 30+42.

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; a+=PrimeNextTwinAverage[a]; If[PrimeQ[a-1]&&PrimeQ[a+1], AppendTo[lst, a]]], {n, 8!}]; lst
Select[Total/@Partition[Mean/@Select[Partition[Prime[Range[ 2000]], 2, 1], #[[2]] - #[[1]] ==2&], 2, 1], AllTrue[#+{1, -1}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 12 2020 *)

Crossrefs

Cf. A014574.

Sequence in context: A039320 A043143 A043923 * A091896 A101140 A287683

Adjacent sequences: A160913 A160914 A160915 * A160917 A160918 A160919

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Extensions

Comment and examples edited by R. J. Mathar, Jul 31 2007

Status

approved