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%I #25 Aug 03 2017 12:43:30
%S 5,11,17,29,37,53,127,149,211,223,307,331,541,1361,1693,1973,2203,
%T 2503,2999,3299,4327,4861,5623,5779,5981,6521,6947,7283,8501,9587,
%U 10007,10831,11777,15727,19661,31469,34123,35671,35729,43391,44351,45943,48731,58889
%N Bounding prime for the first k-Ramanujan prime.
%C The index A277719(n) is h(n), the prime a(n) is p_h(n). If 1 <= n <= 43 and k in [p_{h(n+1)}/p_{h(n+1)-1}, p_{h(n)}/p_{h(n)-1}), then the first k-Ramanujan prime R^{(k)}_1 = p_{h(n)}. Extra terms require improvements of prime numbers in short intervals.
%H Christian Axler and Thomas Leßmann, <a href="http://arxiv.org/abs/1504.05485">An explicit upper bound for the first k-Ramanujan prime</a>, arXiv:1504.05485 [math.NT], 2015.
%H Christian Axler and Thomas Leßmann, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.124.7.642">On the first k-Ramanujan prime</a>, Amer. Math. Monthly, 124 (2017), 642-646.
%e With n = 3, we see p_h(3) = 17, p_h(4) = 29, so that 29/23 <= k < 17/13. If k = 1.3 then R^(1.3)_1 = 17 = p_h(3).
%Y Cf. A277719, A164952, A104272, A290394 (first (1 + 1/n)-Ramanujan prime).
%K nonn
%O 1,1
%A _John W. Nicholson_, Oct 27 2016
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