|
%I #44 Aug 01 2017 12:08:29
%S 2,3,5,13,17,29,31,37,41,53,59,61,71,79,83,97,101,103,107,127,131,137,
%T 149,151,157,173,179,191,193,197,199,223,227,229,239,251,257,269,271,
%U 277,293,307,311,317,337,347,349,359,367,373,379,389,397,419,431,439
%N 0.25-Ramanujan primes R_{0.25,n}: a(n) is the smallest number such that for any x >= a(n), we have pi(x) - pi(0.25x) >= n, where pi(x) is the number of primes <= x.
%C Generalized Ramanujan primes with the parameter k have been introduced for the first time by Vladimir Shevelev in comment to A164952 from Sep 01 2009 (see also his comment to A104272 from the same date). Amersi et al. give the same definition with the parameter c=1/k in their cited paper. - _Vladimir Shevelev_, Aug 18 2011
%C See additional comments and links in A290394. - _Jonathan Sondow_, Aug 01 2017
%H N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, J. Sondow, <a href="http://arxiv.org/abs/1108.0475">Generalized Ramanujan primes</a>, arXiv:1108.0475 [math.NT], 2011.
%H N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, J. Sondow, <a href="https://doi.org/10.1007/978-1-4939-1601-6_1">Generalized Ramanujan primes</a>, Combinatorial and Additive Number Theory, Springer Proc. in Math. & Stat., CANT 2011 and 2012, Vol. 101 (2014), 1-13
%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 V. Shevelev, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL15/Shevelev/shevelev19.html">Ramanujan and Labos primes, their generalizations, and classifications of primes</a>, J. Integer Seq. 15 (2012) Article 12.5.4
%F a(n) <= A104272(n).
%Y Cf. A104272 (Ramanujan primes), A193880 (0.75-Ramanujan primes), A164952, A290394 (first (1 + 1/n)-Ramanujan prime).
%K nonn
%O 1,1
%A _Nadine Amersi_, Olivia Beckwith (obeckwith(AT)gmail.com), Steven J. Miller (Steven.J.Miller(AT)williams.edu), Ryan Ronan (ronan2(AT)cooper.edu), _Jonathan Sondow_ Aug 04 2011
|
