A189027 There appear to be at least n primes in the range (x-2*sqrt(x), x] for all x >= a(n).

2, 3, 37, 139, 331, 1409, 1423, 1427, 2239, 3163, 3181, 3511, 6547, 7433, 7457, 7487, 10061, 11777, 11779, 14401, 18899, 19081, 19373, 23537, 24763, 27617, 27673, 32027, 32051, 38113, 43573, 43579, 47269, 47279, 50839, 61463, 88643, 88651, 88657, 88729

Offset: 1

Author

T. D. Noe, Apr 15 2011

Keywords

• nonn

Comments

These terms exist only if a strong form of Legendre's conjecture that there is a prime between consecutive squares is true. Note that every term is prime. Sequence A189025 gives the number of primes in the range (x-2*sqrt(x), x]. The index of prime a(n), that is, primepi(a(n)), is approximately (5n)^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, Legendre's conjecture

Crossrefs

Cf. A189024, A189026.