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4-Ramanujan primes; the interval (x/2,x] has at least n 3-Ramanujan primes for x >= a(n) but not for x = a(n)-1.
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%I #17 Aug 22 2012 00:20:27

%S 569,571,587,1367,1373,1423,1439,2207,2237,2239,2267,2269,2273,3251,

%T 3257,3259,3299,3343,3347,3449,3581,3583,3607,5639,5641,5647,5651,

%U 5653,5689,5693,5737,5779,5783,5821,8059,8069,8209,8527,8537,8597,8599,8731,8747

%N 4-Ramanujan primes; the interval (x/2,x] has at least n 3-Ramanujan primes for x >= a(n) but not for x = a(n)-1.

%C It is conjectured that primepi(a(n)) < 22*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 27 2011

%C Subsequence of the 3-Ramanujan primes A192821, by the minimality of a(n). - _Jonathan Sondow_, Aug 21 2012

%Y Cf. A104272 (Ramanujan primes), A192820, A192821 (3-Ramanujan primes), A192823, A192824.

%K nonn

%O 1,1

%A _T. D. Noe_, Jul 11 2011

%E Definition clarified by _Jonathan Sondow_, Aug 21 2012