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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)



Shevelev, Greathouse, and Moses (2012) prove that if more terms exist, they are >= 5*10^7.


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.


a(n) = k for some n <=> A218831(k) = 0. - Jonathan Sondow, Aug 04 2017


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.


Cf. A104272, A218831.

Sequence in context: A186946 A057225 A309289 * A070819 A195667 A005244

Adjacent sequences: A220312 A220313 A220314 * A220316 A220317 A220318




Jonathan Sondow, Dec 13 2012



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Last modified December 7 05:31 EST 2022. Contains 358649 sequences. (Running on oeis4.)