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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.
11

%I #38 Nov 11 2018 07:04:25

%S 2,11,17,29,41,47,59,67,71,97,101,107,109,137,151,167,179,181,191,197,

%T 233,239,241,263,269,281,283,311,347,349,367,373,401,409,419,431,433,

%U 439,461,487,491,503,521,571,587,593,599,601,607,617,643,647,653

%N 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 The next prime after a(n) is A080359(n+1).

%H Alois P. Heinz, <a href="/A194658/b194658.txt">Table of n, a(n) for n = 1..1000</a>

%H 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 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 A080359(n) <= a(n) <= A104272(n).

%t b[1] = 2; b[n_] := b[n] = Module[{x = b[n-1]}, While[PrimePi[x] - PrimePi[ Quotient[x, 2]] != n, x++]; x];

%t a[n_] := NextPrime[b[n+1], -1];

%t Array[a, 100] (* _Jean-François Alcover_, Nov 11 2018 *)

%Y Subsequence of A164368.

%Y Cf. A080359, A193507, A104272.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Sep 01 2011