A220273 a(n) is the smallest number, such that for all N >= a(n) there are at least n primes between 5*N and 6*N.

2, 7, 17, 24, 25, 38, 41, 58, 59, 64, 65, 73, 95, 97, 103, 106, 107, 108, 138, 143, 143, 157, 169, 169, 174, 179, 182, 214, 227, 238, 239, 242, 248, 267, 267, 268, 269, 269, 329, 330, 333, 336, 343, 348, 353, 368, 379, 379, 383, 389, 392, 432, 437, 437, 444

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, J. Sondow, Generalized Ramanujan primes, arXiv 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, J. Integer Seq. 15 (2012) Article 12.5.4

Vladimir Shevelev, Charles R. Greathouse IV, Peter J. C. Moses, On intervals (kn, (k+1)n) containing a prime for all n>1, Journal of Integer Sequences, Vol. 16 (2013), Article 13.7.3. arXiv:1212.2785

Formula

a(n) <= ceiling(R_(6/5)(n)/6), where R_v(n) (v>1) are generalized Ramanujan numbers (see Shevelev's link). In particular, for n >= 1, {R_(6/5)(n)}={29, 59, 137, 139, 149, 223, 241, 347, 353, 383, 389, 563, 569, 593, ...}. Moreover, if R_(6/5)(n) == 1 (mod 6), then a(n) = ceiling(R_(6/5)(n)/6).

Crossrefs

Cf. A084140, A220268, A220269.

Sequence in context: A215823 A049542 A049582 * A276698 A260801 A031377

Adjacent sequences: A220270 A220271 A220272 * A220274 A220275 A220276

Keyword

nonn

Author

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

Status

approved