

A193880


0.75Ramanujan primes R_{0.75,n}: a(n) is the smallest number such that for all x >= a(n), we have pi(x)  pi(0.75x) >= n, where pi(x) is the number of primes <= x.


3



11, 29, 59, 67, 101, 149, 157, 163, 191, 227, 269, 271, 307, 379, 383, 419, 431, 433, 443, 457, 563, 593, 601, 641, 643, 673, 701, 709, 733, 827, 829, 907, 937, 947, 971, 1019, 1033, 1039, 1051, 1087, 1187, 1193, 1217, 1277, 1427, 1429, 1433, 1481, 1483, 1487
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OFFSET

1,1


COMMENTS

See comment to A193761.  Vladimir Shevelev, Aug 18 2011


LINKS

Table of n, a(n) for n=1..50.
N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, J. Sondow, Generalized Ramanujan primes
N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, J. Sondow, Generalized Ramanujan primes, Combinatorial and Additive Number Theory, Springer Proc. in Math. & Stat., CANT 2011 and 2012, Vol. 101 (2014), 113
V. Shevelev, Ramanujan and Labos primes, their generalizations and classifications of primes
V. Shevelev, Ramanujan and Labos primes, their generalizations, and classifications of primes, J. Integer Seq. 15 (2012) Article 12.5.4


FORMULA

a(n) >= A104272(n)


CROSSREFS

Cf. A104272 Ramanujan primes, A193761 0.25Ramanujan primes, A164952.
Sequence in context: A024846 A024842 A031072 * A138248 A054692 A056256
Adjacent sequences: A193877 A193878 A193879 * A193881 A193882 A193883


KEYWORD

nonn


AUTHOR

Nadine Amersi, Olivia Beckwith (obeckwith(AT)gmail.com), Steven J. Miller (Steven.J.Miller(AT)williams.edu), Ryan Ronan (ronan2(AT)cooper.edu), Jonathan Sondow, Aug 07 2011


STATUS

approved



