A192822 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.

569, 571, 587, 1367, 1373, 1423, 1439, 2207, 2237, 2239, 2267, 2269, 2273, 3251, 3257, 3259, 3299, 3343, 3347, 3449, 3581, 3583, 3607, 5639, 5641, 5647, 5651, 5653, 5689, 5693, 5737, 5779, 5783, 5821, 8059, 8069, 8209, 8527, 8537, 8597, 8599, 8731, 8747

Offset: 1

Author

T. D. Noe, Jul 11 2011

Keywords

• nonn

Comments

It is conjectured that primepi(a(n)) < 22*n for large n. - T. D. Noe, Aug 26 2011

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

Subsequence of the 3-Ramanujan primes A192821, by the minimality of a(n). - Jonathan Sondow, Aug 21 2012

Crossrefs

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

Extensions

Definition clarified by Jonathan Sondow, Aug 21 2012