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%I #8 Dec 21 2016 17:45:13
%S 7,11,13,23,29,31,53,83,101,109,113,149,181,211,223,293,331,353,379,
%T 431,449,461,571,599,643,659,661,673,709,743,919,1021,1039,1051,1123,
%U 1151,1231,1249,1319,1429,1439,1483,1553,1579,1583,1619,1723,1931,2069,2143
%N Primes p such that 6*(p-6) is an average of a twin prime pair.
%C Primes of the form 6+A014574(k)/6, any k.
%H G. C. Greubel, <a href="/A163388/b163388.txt">Table of n, a(n) for n = 1..1100</a>
%e For p=7, 6*(7-6)=6 = A014574(2), which puts 7 into the sequence.
%e For p=11, 6*(11-6)=30 = A014574(5), which puts p=11 into the sequence.
%t f1[n_]:=If[PrimeQ[n-1]&&PrimeQ[n+1],True,False]; f2[n_]:=If[f1[n]&&PrimeQ[n/ 6+6],True,False]; lst={};Do[If[f2[n],AppendTo[lst,n/6+6]],{n,8!}]; lst
%Y Cf. A163385, A163386, A163387
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 25 2009
%E Definition rephrased, reference to A014574 added by _R. J. Mathar_, Aug 02 2009
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