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A166252 Primes which are not the smallest or largest prime in an interval of the form (2*prime(k),2*prime(k+1)).

%I A166252 #19 Jun 01 2023 22:32:40
%S A166252 71,101,109,151,181,191,229,233,239,241,269,283,311,349,373,409,419,
%T A166252 433,439,491,571,593,599,601,607,643,647,653,659,683,727,823,827,857,
%U A166252 941,947,991,1021,1031,1033,1051,1061,1063,1091,1103,1301,1373,1427,1429
%N A166252 Primes which are not the smallest or largest prime in an interval of the form (2*prime(k),2*prime(k+1)).
%C A166252 Called "central primes" in A166251, not to be confused with the central polygonal primes A055469.
%C A166252 The primes tabulated in intervals (2*prime(k),2*prime(k+1)) are
%C A166252 5, k=1
%C A166252 7, k=2
%C A166252 11,13, k=3
%C A166252 17,19, k=4
%C A166252 23,    k=5
%C A166252 29,31, k=6
%C A166252 37,    k=7
%C A166252 41,43, k=8
%C A166252 47,53, k=9
%C A166252 59,61, k=10
%C A166252 67,71,73,  k=11
%C A166252 79,        k=12
%C A166252 83,     k=13
%C A166252 89,     k=14
%C A166252 97,101,103, k=15
%C A166252 and only rows with at least 3 primes contribute primes to the current sequence.
%C A166252 For n >= 2, these are numbers of A164368 which are in A194598. - Vladimir Shevelev, Apr 27 2012
%H A166252 T. D. Noe, <a href="/A166252/b166252.txt">Table of n, a(n) for n = 1..1000</a>
%e A166252 Since 2*31 < 71 < 2*37 and the interval (62, 74) contains prime 67 < 71 and prime 73 > 71, then 71 is in the sequence.
%t A166252 n = 0; t = {}; While[Length[t] < 100, n++; ps = Select[Range[2*Prime[n], 2*Prime[n+1]], PrimeQ]; If[Length[ps] > 2, t = Join[t, Rest[Most[ps]]]]]; t (* _T. D. Noe_, Apr 30 2012 *)
%Y A166252 Cf. A166307, A182365, A166251, A164368, A104272, A080359, A164333, A164288, A164294, A164554, A194598.
%K A166252 nonn
%O A166252 1,1
%A A166252 _Vladimir Shevelev_, Oct 10 2009, Oct 14 2009