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

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A014574.

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;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 *)

Extensions

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