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A193761 0.25-Ramanujan primes R_{0.25,n}: a(n) is the smallest number such that for any x >= a(n), we have pi(x) - pi(0.25x) >= n, where pi(x) is the number of primes <= x. 2
2, 3, 5, 13, 17, 29, 31, 37, 41, 53, 59, 61, 71, 79, 83, 97, 101, 103, 107, 127, 131, 137, 149, 151, 157, 173, 179, 191, 193, 197, 199, 223, 227, 229, 239, 251, 257, 269, 271, 277, 293, 307, 311, 317, 337, 347, 349, 359, 367, 373, 379, 389, 397, 419, 431, 439 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Generalized Ramanujan primes with the parameter k have been introduced for the first time by Vladimir Shevelev in comment to A164952 from Sep 01 2009 (see also his comment to A104272 from the same date). Amersi et al. give the same definition with the parameter c=1/k in their cited paper. - Vladimir Shevelev, Aug 18 2011

LINKS

Table of n, a(n) for n=1..56.

N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, J. Sondow, Generalized Ramanujan Primes

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), A193880 (0.75-Ramanujan primes), A164952.

Sequence in context: A214802 A215318 A186945 * A215355 A242752 A215813

Adjacent sequences:  A193758 A193759 A193760 * A193762 A193763 A193764

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 04 2011

STATUS

approved

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Last modified October 2 10:33 EDT 2014. Contains 247538 sequences.