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URL: https://oeis.org/A220268

⇱ A220268 - OEIS

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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
OFFSET
1,1
LINKS
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
KEYWORD
nonn
STATUS
approved