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%I #34 Oct 22 2023 13:27:51
%S 11,9433,9437,62983,62987,72229,72251,392269,392279,495589,495611,
%T 663583,663587,909301,909317,909319,909329,1006309,1006331,1138393,
%U 1138409,1159201,1159229,1173553,1173581,1322161,1322171,2144491
%N Prime in the middle of a list of 7 consecutive primes such that each of them is a member of a twin pair.
%C This is roughly a search for at least three successive zeros in A048614.
%e The twin prime 9433 is in the sequence because it is in the middle of the list of 7 successive primes 9419, 9421, 9431, 9433, 9437, 9439, 9461, of which each is a member of a twin prime pair.
%t tp7Q[lst_]:=Total[If[PrimeQ[#+2]||PrimeQ[#-2],1,0]&/@lst]==7; Select[Partition[Prime[ Range[ 160000]],7,1],tp7Q][[;;,4]] (* _Harvey P. Dale_, Oct 22 2023 *)
%Y Cf. A001097, A048614.
%K nonn
%O 1,1
%A _Irina Gerasimova_, Jun 30 2013