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3-Ramanujan primes; the interval (x/2,x] has at least n 2-Ramanujan primes for x >= a(n) but not for x = a(n)-1.
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%I #27 Aug 22 2012 00:20:07

%S 41,149,227,229,233,569,571,587,593,641,643,821,937,941,1367,1373,

%T 1423,1439,1481,1549,1553,2207,2237,2239,2267,2269,2273,2281,2333,

%U 2339,2347,2377,2617,2657,3251,3257,3259,3299,3343,3347,3449,3581,3583,3607,3613

%N 3-Ramanujan primes; the interval (x/2,x] has at least n 2-Ramanujan primes for x >= a(n) but not for x = a(n)-1.

%C It is conjectured that primepi(a(n)) < 10*n for large n. - T. D. Noe, Aug 26 2011

%C The sequence is only conjectural without a proof of an upper bound on a(n) (like the bound A104272(n) < prime(3*n) proved by Laishram and used in computing Ramanujan primes). - _Jonathan Sondow_, Aug 26 2011

%C Subsequence of the 2-Ramanujan primes A192820, by the minimality of a(n). - _Jonathan Sondow_, Aug 21 2012

%Y Cf. A104272 (Ramanujan primes), A192820 (2-Ramanujan primes), A192822, A192823, A192824.

%K nonn

%O 1,1

%A _T. D. Noe_, Jul 11 2011

%E Definition clarified by _Jonathan Sondow_, Aug 21 2012