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A160916
Averages of twin prime pairs which are a sum of averages of two consecutive twin prime pairs.
4
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Comment and examples edited by R. J. Mathar, Jul 31 2007
STATUS
approved