A192823 5-Ramanujan primes; the interval (x/2,x] has at least n 4-Ramanujan primes for x >= a(n) but not for x = a(n)-1.

1367, 1373, 1423, 1439, 2207, 2237, 3251, 3257, 3259, 3299, 5639, 8059, 12739, 12781, 12799, 12809, 12821, 12823, 12829, 12907, 12911, 12917, 12919, 12953, 13147, 13163, 13171, 13669, 13687, 13691, 13693, 14009, 14029, 14057, 14081, 14143, 31957, 32183

Offset: 1

Author

T. D. Noe, Jul 11 2011

Keywords

• nonn

Comments

It is conjectured that primepi(a(n)) < 50*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 4-Ramanujan primes A192822, by the minimality of a(n). - Jonathan Sondow, Aug 21 2012

Crossrefs

Cf. A104272 (Ramanujan primes), A192820, A192821, A192822 (4-Ramanujan primes), A192824.

Extensions

Definition clarified by Jonathan Sondow, Aug 21 2012