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 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). 2
 1, 2490, 567, 756, 425, 510, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. 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 LINKS Christian Axler, On the number of primes up to the n-th Ramanujan prime, arXiv:1711.04588 [math.NT], 2017. J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2. Shichun Yang and Alain Togbé, On the estimates of the upper and lower bounds of Ramanujan primes, Ramanujan J., online 14 August 2015, 1-11. FORMULA For all n >= 20, a(n) = 2*n. CROSSREFS Cf. A104272, A179196, A190413. Sequence in context: A255757 A254839 A231456 * A248548 A252315 A131523 Adjacent sequences: A190411 A190412 A190413 * A190415 A190416 A190417 KEYWORD nonn AUTHOR John W. Nicholson, May 10 2011 STATUS approved

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Last modified February 3 08:31 EST 2023. Contains 360034 sequences. (Running on oeis4.)