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
Keywords
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).