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 A220274 #40 Feb 24 2025 12:52:37
%S A220274 2,14,23,23,34,36,57,58,60,60,77,86,100,100,102,123,149,149,149,149,
%T A220274 187,187,200,200,200,202,209,227,234,268,269,269,270,319,319,331,332,
%U A220274 332,333,345,347,350,350,353,359,360,377,401,421,440,449,479,479,487,491
%N A220274 a(n) is the smallest number such that for all N >= a(n) there are at least n primes between 9*N and 10*N.
%H A220274 Peter J. C. Moses, <a href="/A220274/b220274.txt">Table of n, a(n) for n = 1..3000</a>
%H A220274 N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, and J. Sondow, <a href="http://arxiv.org/abs/1108.0475">Generalized Ramanujan primes</a>, arXiv:1108.0475 [math.NT], 2011.
%H A220274 N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, and 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 A220274 Vladimir 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
%H A220274 Vladimir Shevelev, Charles R. Greathouse IV, and Peter J. C. Moses, <a href="http://arxiv.org/abs/1212.2785">On intervals (kn, (k+1)n) containing a prime for all n>1</a>, arXiv:1212.2785 [math.NT], 2012.
%F A220274 a(n) <= ceiling(R_(10/9)(n)/10), where R_v(n) (v>1) are generalized Ramanujan numbers (see Shevelev's link). In particular, for n >= 1, {R_(10/9) (n)} = {127, 223, 227, 269, 349, 359, 569, 587, 593, 739, 809, 857, 991, 1009, ...}. Moreover, if R_(10/9)(n) == 1 (mod 10), then a(n) = ceiling(R_(10/9)(n)/10).
%Y A220274 Cf. A084140, A220268, A220269, A220273.
%K A220274 nonn
%O A220274 1,1
%A A220274 _Vladimir Shevelev_, _Charles R Greathouse IV_, and _Peter J. C. Moses_, Dec 09 2012