This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A190413 #43 Sep 12 2019 12:28:48
%S A190413 1,1245,189,189,85,85,10,10,10,10,10,10,10,10,10,10,10,10,10,2,2,2,2,
%T A190413 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A190413 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A190413 primepi(R_{n*m}) <= n*primepi(R_m) for m >= a(n), where R_k is the k-th Ramanujan prime (A104272).
%C A190413 This is Conjecture 1 in the paper by Sondow, Nicholson, and Noe. The conjecture has been verified for n <= 20 and Ramanujan primes less than 10^9.
%C A190413 A restatement is rho(n*m) <= n*rho(m) for m >= a(n), where rho = A179196.
%C A190413 The conjecture has been proven for n > 10^300 by Shichun Yang and Alain Togbé. - _Jonathan Sondow_, Jan 21 2016
%C A190413 The conjecture has been proven for n > 38 and m > 9 by Christian Axler. Complete exception list can be found in remark of paper. - _John W. Nicholson_, Aug 04 2019
%H A190413 Christian Axler, <a href="https://arxiv.org/abs/1711.04588">On the number of primes up to the n-th Ramanujan prime</a>, arXiv:1711.04588 [math.NT], 2017.
%H A190413 J. Sondow, <a href="http://arxiv.org/abs/0907.5232"> Ramanujan primes and Bertrand's postulate</a>, Amer. Math. Monthly 116 (2009) 630-635.
%H A190413 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>, J. Integer Seq. 14 (2011) Article 11.6.2.
%H A190413 Shichun Yang and Alain Togbé, <a href="http://dx.doi.org/10.1007/s11139-015-9706-8">On the estimates of the upper and lower bounds of Ramanujan primes</a>, Ramanujan J., online 14 August 2015, 1-11.
%F A190413 For all n >= 20, a(n) = 2.
%Y A190413 Cf. A007395, A104272, A179196, A190414.
%K A190413 nonn,easy
%O A190413 1,2
%A A190413 _T. D. Noe_, May 11 2011