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A189026
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There appear to be at least n primes in the range (x-sqrt(x), x] for all x >= a(n).
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4
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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
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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 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).
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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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