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A220274 a(n) is the smallest number such that for all N >= a(n) there are at least n primes between 9*N and 10*N. 3
2, 14, 23, 23, 34, 36, 57, 58, 60, 60, 77, 86, 100, 100, 102, 123, 149, 149, 149, 149, 187, 187, 200, 200, 200, 202, 209, 227, 234, 268, 269, 269, 270, 319, 319, 331, 332, 332, 333, 345, 347, 350, 350, 353, 359, 360, 377, 401, 421, 440, 449, 479, 479, 487, 491 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..3000

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

N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, and J. Sondow, Generalized Ramanujan primes, Combinatorial and Additive Number Theory, Springer Proc. in Math. & Stat., CANT 2011 and 2012, Vol. 101 (2014), 1-13

Vladimir Shevelev, Ramanujan and Labos primes, their generalizations, and classifications of primes, J. Integer Seq. 15 (2012) Article 12.5.4

Vladimir Shevelev, –°harles R. Greathouse IV, and Peter J. C. Moses, On intervals (kn, (k+1)n) containing a prime for all n>1, arXiv:1212.2785 [math.NT], 2012.

FORMULA

a(n) <= ceiling(R_(10/9)(n)/10), where R_v(n) (v>1) are generalized Ramanujan numbers (see Shevelev's link). In particular, for n >= 1, {R_(10/9) (n)} = {127, 223, 227, 269, 349, 359, 569, 587, 593, 739, 809, 857, 991, 1009, ...}. Moreover, if R_(10/9)(n) == 1 (mod 10), then a(n) = ceiling(R_(10/9)(n)/10).

CROSSREFS

Cf. A084140, A220268, A220269, A220273.

Sequence in context: A069512 A328217 A116639 * A036433 A172048 A226334

Adjacent sequences:  A220271 A220272 A220273 * A220275 A220276 A220277

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Charles R Greathouse IV, and Peter J. C. Moses, Dec 09 2012

STATUS

approved

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Last modified September 18 01:54 EDT 2021. Contains 347504 sequences. (Running on oeis4.)