

A190414


primepi(R_m) <= i*primepi(R_j) for any factorization m=i*j if j >= a(i), where R_k is the kth 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
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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

Table of n, a(n) for n=1..50.
Christian Axler, On the number of primes up to the nth 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, 111.


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



