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, 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

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, Сharles 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