A189993 Length of the longest run of Ramanujan primes that are consecutive primes < 10^n.

1, 2, 5, 13, 13, 20, 21, 26, 31

Offset

1,2

Links

Table of n, a(n) for n=1..9.

Jonathan Sondow, Ramanujan primes and Bertrand's postulate, arXiv:0907.5232 [math.NT], 2009-2010; Amer. Math. Monthly 116 (2009), 630-635.

Jonathan Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2.

Example

In the sequence of primes < 10^3, there is a run of 5 Ramanujan primes, but no longer run, so a(3) = 5.

Crossrefs

Cf. A104272 (Ramanujan primes), A189994 (length of the longest run of non-Ramanujan primes < 10^n), A174602 (smallest prime that begins a run of n Ramanujan primes).

Sequence in context: A166134 A336883 A067365 * A112838 A111296 A089728

Adjacent sequences: A189990 A189991 A189992 * A189994 A189995 A189996

Keyword

nonn

Author

Jonathan Sondow, May 03 2011

Status

approved