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A132992
Twin prime pair averages n such that 3*n and 9*n are also averages of twin prime pairs.
1
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited and extended by Klaus Brockhaus, Dec 04 2009
STATUS
approved