A189026 There appear to be at least n primes in the range (x-sqrt(x), x] for all x >= a(n).

127, 1367, 2531, 2539, 6007, 7457, 10061, 10847, 23531, 35797, 35801, 38557, 44497, 47111, 69767, 69809, 88321, 107687, 110419, 110431, 113723, 127217, 250673, 250681, 250687, 250703, 268487, 268493, 286381, 286393, 302563, 302567, 360947, 369821, 405199

Offset: 1

Author

T. D. Noe, Apr 15 2011

Keywords

• nonn

Comments

These terms exist only if a strong form of Oppermann's conjecture that for any k>1 there is a prime between k^2-k and k^2 is true. Note that every term is prime. Sequence A189024 gives the number of primes in the range (x-sqrt(x), x]. The index of the prime a(n), that is, primepi(a(n)), is approximately (2.4*n)^2. These primes are generated in a manner similar to the Ramanujan primes (A104272).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Wikipedia, Oppermann's conjecture

Crossrefs

Cf. A189025, A189027.