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A190414
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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).
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2
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=1..50.
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.
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FORMULA
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For all n >= 20, a(n) = 2*n.
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CROSSREFS
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Cf. A104272, A179196, A190413.
Sequence in context: A255757 A254839 A231456 * A248548 A252315 A131523
Adjacent sequences: A190411 A190412 A190413 * A190415 A190416 A190417
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KEYWORD
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nonn
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AUTHOR
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John W. Nicholson, May 10 2011
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STATUS
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approved
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