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

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A014574, A160916, A160917.

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;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 *)

Formula

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