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%I #33 Sep 12 2019 12:27:10
%S 1,2490,567,756,425,510,70,80,90,100,110,120,130,140,150,160,170,180,
%T 190,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,
%U 82,84,86,88,90,92,94,96,98,100
%N 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 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 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 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 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 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 For all n >= 20, a(n) = 2*n.
%Y Cf. A104272, A179196, A190413.
%K nonn
%O 1,2
%A _John W. Nicholson_, May 10 2011
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