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A132929 Averages of twin primes such that the sum of the lower, average and upper parts of the twin primes are averages of other twin primes.

%I A132929 #11 May 03 2022 10:44:28
%S A132929 4,6,60,270,1950,3000,6360,11490,11550,14550,18540,19890,21840,31080,
%T A132929 32910,32970,33330,33600,42570,42840,50460,53550,58110,68880,70200,
%U A132929 74610,79230,80910,93810,96330,98910,104310,109140,114600,121020,125790
%N A132929 Averages of twin primes such that the sum of the lower, average and upper parts of the twin primes are averages of other twin primes.
%H A132929 Amiram Eldar, <a href="/A132929/b132929.txt">Table of n, a(n) for n = 1..10000</a>
%F A132929 From _Wesley Ivan Hurt_, May 03 2022: (Start)
%F A132929 a(n) = A174920(n) + 1.
%F A132929 a(n) = A177336(n) - 1. (End)
%e A132929 4 is a term since (3, 5) are twin primes, 3 + 4 + 5 = 12 and (11, 13) are also twin primes.
%e A132929 6 is a term since (5, 7) are twin primes, 5 + 6 + 7 = 18 and (17, 19) are also twin primes.
%t A132929 TwinPrimeAverageQ[n_]:=If[PrimeQ[n-1]&&PrimeQ[n+1],True,False](*TwinPrimeAverageQ*) lst={};Do[If[TwinPrimeAverageQ[n],If[TwinPrimeAverageQ[3*n],(*Print[n];*)AppendTo[lst,n]]],{n,9!}];lst
%Y A132929 Cf. A014574.
%Y A132929 Cf. A174920, A177336.
%K A132929 nonn
%O A132929 1,1
%A A132929 _Vladimir Joseph Stephan Orlovsky_, Aug 26 2008