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A189027
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There appear to be at least n primes in the range (x-2*sqrt(x), x] for all x >= a(n).
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4
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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
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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