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

1,1

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.

Formula

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

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 *)

Crossrefs

Subsequence of A164368.

Cf. A080359, A193507, A104272.

Sequence in context: A087379 A019364 A164368 * A104272 A214934 A233866

Adjacent sequences: A194655 A194656 A194657 * A194659 A194660 A194661

Keyword

nonn

Author

Vladimir Shevelev, Sep 01 2011

Status

approved