A160917 Averages of twin prime pairs which can be represented as a sum of three consecutive of such pair averages.

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

Cf. A014574, A160916, A160918.

Sequence in context: A333966 A059461 A328156 * A100154 A246230 A100148

Adjacent sequences: A160914 A160915 A160916 * A160918 A160919 A160920

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Extensions

Comments moved to the examples - R. J. Mathar, Sep 11 2009

Status

approved