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.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
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
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
Sequence in context: A186946 A057225 A309289 * A070819 A195667 A005244
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.

License Agreements, Terms of Use, Privacy Policy. .

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