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A194658 a(n) is the maximal prime, such that for all primes x<=a(n) the number of primes in (x/2,x) is less than n.

%I A194658 #38 Nov 11 2018 07:04:25
%S A194658 2,11,17,29,41,47,59,67,71,97,101,107,109,137,151,167,179,181,191,197,
%T A194658 233,239,241,263,269,281,283,311,347,349,367,373,401,409,419,431,433,
%U A194658 439,461,487,491,503,521,571,587,593,599,601,607,617,643,647,653
%N A194658 a(n) is the maximal prime, such that for all primes x<=a(n) the number of primes in (x/2,x) is less than n.
%C A194658 The next prime after a(n) is A080359(n+1).
%H A194658 Alois P. Heinz, <a href="/A194658/b194658.txt">Table of n, a(n) for n = 1..1000</a>
%H A194658 V. Shevelev, <a href="http://arxiv.org/abs/0909.0715">Ramanujan and Labos primes, their generalizations and classifications of primes</a>, arXiv:0909.0715 [math.NT], 2009-2011.
%H A194658 J. Sondow, J. W. Nicholson, and T. D. Noe, <a href="http://arxiv.org/abs/1105.2249"> Ramanujan Primes: Bounds, Runs, Twins, and Gaps</a>, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2.
%F A194658 A080359(n) <= a(n) <= A104272(n).
%t A194658 b[1] = 2; b[n_] := b[n] = Module[{x = b[n-1]}, While[PrimePi[x] - PrimePi[ Quotient[x, 2]] != n, x++]; x];
%t A194658 a[n_] := NextPrime[b[n+1], -1];
%t A194658 Array[a, 100] (* _Jean-François Alcover_, Nov 11 2018 *)
%Y A194658 Subsequence of A164368.
%Y A194658 Cf. A080359, A193507, A104272.
%K A194658 nonn
%O A194658 1,1
%A A194658 _Vladimir Shevelev_, Sep 01 2011