A193880 0.75-Ramanujan 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.

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

Offset

1,1

Comments

See comment to A193761. - Vladimir Shevelev, Aug 18 2011

See additional comments and links in A290394. - Jonathan Sondow, Aug 01 2017

Links

Table of n, a(n) for n=1..50.

N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, J. Sondow, Generalized Ramanujan primes, arXiv:1108.0475 [math.NT], 2011.

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), 1-13

V. Shevelev, Ramanujan and Labos primes, their generalizations and classifications of primes, arXiv:0909.0715 [math.NT], 2009-2011.

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).

Example

a(1) = A290394(3) = 11. - Jonathan Sondow, Aug 01 2017

Crossrefs

Cf. A104272 (Ramanujan primes), A193761 (0.25-Ramanujan primes), A164952, A290394 (first (1 + 1/n)-Ramanujan prime).

Sequence in context: A024842 A304275 A031072 * A138248 A361484 A054692

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