A132992 Twin prime pair averages n such that 3*n and 9*n are also averages of twin prime pairs.

32970, 180180, 273000, 633570, 879690, 991620, 1189650, 2219490, 3229380, 4111170, 4515630, 7384440, 7392630, 7398930, 7431270, 9022440, 9861390, 12183360, 12307680, 12866280, 14619990, 14717640, 14917560, 15458100

Offset

1,1

Links

K. Brockhaus, Table of n, a(n) for n = 1..384.

Example

32970, 3*32970 = 98910, 9*32970 = 296730 are averages of twin prime pairs.

Mathematica

TwinPrimeAverageQ[n_]:=If[PrimeQ[n-1]&&PrimeQ[n+1], True, False](*TwinPrimeAverageQ*)lst={}; Do[If[TwinPrimeAverageQ[n], If[TwinPrimeAverageQ[3*n], If[TwinPrimeAverageQ[9*n], (*Print[n]; *)AppendTo[lst, n]]]], {n, 7!, 3*10!}]; lst
atppQ[n_]:=And@@PrimeQ[{3n-1, 3n+1, 9n-1, 9n+1}]; Select[Mean/@Select[ Partition[ Prime[Range[10^6]], 2, 1], #[[2]]-#[[1]]==2&], atppQ] (* Harvey P. Dale, Jul 06 2014 *)

Prog

(Magma) [ a: p in PrimesUpTo(16000000) | IsPrime(a+1) and IsPrime(3*a-1) and IsPrime(3*a+1) and IsPrime(9*a-1) and IsPrime(9*a+1) where a is p+1 ]; // Klaus Brockhaus, Dec 04 2009

Crossrefs

Cf. A014574 (average of twin prime pairs).

Sequence in context: A353019 A170780 A251407 * A153748 A170789 A366515

Adjacent sequences: A132989 A132990 A132991 * A132993 A132994 A132995

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Aug 26 2008

Extensions

Edited and extended by Klaus Brockhaus, Dec 04 2009

Status

approved