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 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. 4
 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 (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, 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

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Last modified May 29 15:14 EDT 2023. Contains 363042 sequences. (Running on oeis4.)