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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. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The next prime after a(n) is A080359(n+1).
LINKS
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.
Sequence in context: A087379 A019364 A164368 * A104272 A214934 A233866
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 01 2011
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)