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A160917
Averages of twin prime pairs which can be represented as a sum of three consecutive of such pair averages.
3
60, 282, 348, 522, 570, 618, 1788, 2112, 4050, 4422, 5880, 6198, 8232, 9678, 10458, 11700, 12072, 12162, 12378, 14010, 16140, 17598, 17838, 21648, 22698, 33348, 36342, 39228, 41610, 43782, 44088, 46272, 48780, 51198, 53088, 56910, 58230
OFFSET
1,1
COMMENTS
Values A014574(j) of the form A014574(k)+A014574(k+1)+A014574(k+2).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
EXAMPLE
a(1) = 60 = A014574(7) = 12 + 18 + 30 = A014574(3) + A014574(4) + A014574(5).
a(2) = 282 = A014574(19) = 72 + 102 + 108 = A014574(8) + A014574(9) + A014574(10).
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]; a=a+b+c; If[PrimeQ[a-1]&&PrimeQ[a+1], AppendTo[lst, a]]], {n, 8!}]; lst
Module[{m=Mean/@Select[Partition[Prime[Range[10000]], 2, 1], #[[2]]-#[[1]] == 2&], t}, t=Total/@Partition[m, 3, 1]; Intersection[m, t]] (* Harvey P. Dale, Mar 06 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Comments moved to the examples - R. J. Mathar, Sep 11 2009
STATUS
approved