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.

2, 11, 17, 29, 41, 47, 59, 67, 71, 97, 101, 107, 109, 137, 151, 167, 179, 181, 191, 197, 233, 239, 241, 263, 269, 281, 283, 311, 347, 349, 367, 373, 401, 409, 419, 431, 433, 439, 461, 487, 491, 503, 521, 571, 587, 593, 599, 601, 607, 617, 643, 647, 653

Offset: 1

Author

Vladimir Shevelev, Sep 01 2011

Keywords

• nonn

Comments

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• V. Shevelev, Ramanujan and Labos primes, their generalizations and classifications of primes, arXiv:0909.0715 [math.NT], 2009-2011.
• J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2.

Crossrefs

Subsequence of A164368.

Cf. A080359, A193507, A104272.

Programs

Mathematica

b[1] = 2; b[n_] := b[n] = Module[{x = b[n-1]}, While[PrimePi[x] - PrimePi[ Quotient[x, 2]] != n, x++]; x];
a[n_] := NextPrime[b[n+1], -1];
Array[a, 100] (* Jean-François Alcover, Nov 11 2018 *)

Formula

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