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 A220268 a(n) is the smallest number, such that for N >= a(n) there are at least n primes between 2*N and 3*N. 6
 2, 5, 13, 14, 23, 25, 33, 43, 46, 58, 60, 61, 71, 77, 80, 88, 103, 104, 116, 123, 127, 144, 145, 148, 150, 160, 163, 181, 188, 196, 200, 203, 206, 214, 218, 237, 247, 253, 263, 266, 270, 275, 276, 287, 313, 323, 333, 340, 344, 347, 350, 354, 363, 365, 388 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 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(1) = 2; for n >= 2, a(n) = ceiling(R_(3/2)(n)/3), where R_v(n) (v>1) are generalized Ramanujan numbers (see Shevelev's link). In particular, for n >= 1, {R_(3/2)(n)} = {2, 13, 37, 41, 67, 73, 97, 127, 137, 173, 179, 181, 211, 229, 239, ...}. MATHEMATICA nn = 60; t = Table[PrimePi[3 n] - PrimePi[2 n], {n, 10*nn}]; Join[{2}, Table[s = Flatten[Position[t, _?(# > n - 1 &)]]; i = Length[s]; While[i > 1 && s[[i]] - s[[i - 1]] == 1, i--]; s[[i]], {n, 2, nn}]] (* T. D. Noe, Dec 12 2012 *) CROSSREFS Cf. A084140. Sequence in context: A089728 A127987 A247543 * A049476 A216889 A334494 Adjacent sequences:  A220265 A220266 A220267 * A220269 A220270 A220271 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 23 18:08 EDT 2022. Contains 353993 sequences. (Running on oeis4.)