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Note that the lower bound, n-2*sqrt(n), is excluded from the count and the upper range, n, is included. The only zero term appears to be a(1). See A189027 for special primes associated with this sequence. This sequence is related to Legendre's conjecture that there is a prime between consecutive squares.

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).

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).