A160918 Averages of twin prime pairs that are sums of 4 consecutive averages of twin prime pairs.

102, 150, 420, 660, 858, 1020, 2310, 2730, 3120, 3390, 5100, 5502, 5850, 6198, 7758, 12540, 13692, 13998, 15360, 17292, 21840, 23688, 25932, 32832, 41520, 43398, 46092, 49032, 49410, 50892, 58152, 61560, 64920, 70878, 72270, 78138, 88818

Offset

1,1

Comments

Members of A014574 which can be written as a sum of 4 consecutive members.

Links

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

Formula

{A014574(i): A014574(i) = Sum_{k=0..3} A014574(j+k) for some k,j}.

Example

102 is in the sequence because it can be written as 12 + 18 + 30 + 42.
150 is in the sequence because it is 18 + 30 + 42 + 60.

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]; d=PrimeNextTwinAverage[c]; a=a+b+c+d; If[PrimeQ[a-1]&&PrimeQ[a+1], AppendTo[lst, a]]], {n, 2*8!}]; lst
With[{tpms=Mean/@Select[Partition[Prime[Range[10000]], 2, 1], #[[2]]- #[[1]] ==2&]}, Total/@Select[Partition[tpms, 4, 1], MemberQ[tpms, Total[#]]&]] (* Harvey P. Dale, Apr 27 2012 *)

Crossrefs

Cf. A014574, A160916, A160917.

Sequence in context: A095637 A023059 A015165 * A145578 A318792 A006316

Adjacent sequences: A160915 A160916 A160917 * A160919 A160920 A160921

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Status

approved