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A220281 a(n) is the smallest number, such that for all N >= a(n) there are at least n primes between 14*N and 15*N. 2
2, 11, 24, 37, 38, 39, 50, 96, 96, 96, 96, 97, 97, 125, 125, 132, 178, 178, 178, 179, 179, 180, 213, 221, 222, 222, 224, 235, 235, 242, 282, 283, 307, 309, 310, 360, 360, 361, 362, 366, 367, 367, 377, 377, 377, 421, 422, 458, 458, 502, 503, 504 (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_(15/14)(n)/15), where R_v(n) (v>1) are generalized Ramanujan numbers (see Shevelev's link). In particular, for n >= 1, {R_(15/14)(n)}={127, 307, 347, 563, 569, 733, 1423, 1427, 1429, 1433, 1439, 1447, ...}. Moreover, if R_(15/14)(n) == 1 or 2 (mod 10), then a(n) = ceiling(R_(15/14)(n)/15).

CROSSREFS

Cf. A084140, A220268, A220269, A220273, A220274.

Sequence in context: A042347 A193245 A041803 * A297545 A256905 A294547

Adjacent sequences:  A220278 A220279 A220280 * A220282 A220283 A220284

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 May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)