The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A220315 Integers k for which the open interval (k*m, (k+1)*m) contains a prime for all m > 1. 1
 1, 2, 3, 5, 9, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Shevelev, Greathouse, and Moses (2012) prove that if more terms exist, they are >= 5*10^7. LINKS Table of n, a(n) for n=1..6. N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, and J. Sondow, Generalized Ramanujan primes, arXiv:1108.0475 [math.NT], 2011. N. Amersi, O. Beckwith, S. J. Miller, R. Ronan, and J. Sondow, Generalized Ramanujan primes, Combinatorial and Additive Number Theory, Springer Proc. in Math. & Stat., CANT 2011 and 2012, Vol. 101 (2014), 1-13. Vladimir Shevelev, Charles R. Greathouse IV, and Peter J. C. Moses, On intervals (kn,(k+1)n) containing a prime for all n>1, arXiv:1212.2785 [math.NT], 2012. J. Sondow, Ramanujan primes and Bertrand's postulate, arXiv:0907.5232 [math.NT], 2009-2010; Amer. Math. Monthly, 116 (2009), 630-635. FORMULA a(n) = k for some n <=> A218831(k) = 0. - Jonathan Sondow, Aug 04 2017 EXAMPLE a(1) = 1 because Bertrand's Postulate (proved by Chebyshev) implies that for any m > 1 there is a prime p with m < p < 2m. CROSSREFS Cf. A104272, A218831. Sequence in context: A186946 A057225 A309289 * A070819 A195667 A005244 Adjacent sequences: A220312 A220313 A220314 * A220316 A220317 A220318 KEYWORD nonn,more AUTHOR Jonathan Sondow, Dec 13 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 30 04:46 EDT 2024. Contains 372958 sequences. (Running on oeis4.)