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Length of the longest run of consecutive primes < 10^n that are not Ramanujan primes.
2

%I #8 Mar 30 2012 19:00:09

%S 3,4,7,13,20,36,47,47,65

%N Length of the longest run of consecutive primes < 10^n that are not Ramanujan primes.

%H J. Sondow, <a href="http://arxiv.org/abs/0907.5232"> Ramanujan primes and Bertrand's postulate</a> Amer. Math. Monthly 116 (2009), 630-635.

%H J. Sondow, J. W. Nicholson, and T. D. Noe, <a href="http://arxiv.org/abs/1105.2249"> Ramanujan Primes: Bounds, Runs, Twins, and Gaps</a>, J. Integer Seq. 14 (2011) Article 11.6.2.

%e Of the 4 primes < 10^1, the last 3 are not Ramanujan primes, so a(1) = 3.

%Y Cf. A104272 (Ramanujan primes), A189993 (length of the longest run of Ramanujan primes < 10^n), A174641 (smallest prime that begins a run of n non-Ramanujan primes).

%K nonn

%O 1,1

%A _Jonathan Sondow_, May 03 2011