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 A190414 #33 Sep 12 2019 12:27:10 %S A190414 1,2490,567,756,425,510,70,80,90,100,110,120,130,140,150,160,170,180, %T A190414 190,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80, %U A190414 82,84,86,88,90,92,94,96,98,100 %N A190414 primepi(R_m) <= i*primepi(R_j) for any factorization m=i*j if j >= a(i), where R_k is the k-th Ramanujan prime (A104272). %C A190414 This is another interpretation of Conjecture 1 in the paper by Sondow, Nicholson, and Noe. The conjecture has been verified for i <= 20 and Ramanujan primes less than 10^9. %C A190414 The conjecture has been proven for i > 38 and j > 9 by Christian Axler. Complete exception list can be found in remark of paper. - _John W. Nicholson_, Aug 04 2019 %H A190414 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 A190414 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 A190414 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 A190414 For all n >= 20, a(n) = 2*n. %Y A190414 Cf. A104272, A179196, A190413. %K A190414 nonn %O A190414 1,2 %A A190414 _John W. Nicholson_, May 10 2011