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A058188
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Number of primes between prime(n) and prime(n) + sqrt(prime(n)), where prime(n) is the n-th prime.
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3
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1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 2, 1, 0, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 1, 3, 4, 3, 2, 2, 1, 2, 3, 3, 4, 3, 3, 2, 1, 1, 3, 2, 1, 1, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3, 2, 4, 3, 4, 3, 3, 4, 4, 3, 3, 2, 2, 3, 4, 3, 3, 3, 2, 2, 1, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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COMMENTS
| Conjecture: if prime(n)>=127, there is always at least one prime between prime(n) and prime(n) + sqrt(prime(n)). Easily checked for prime(n)<1.1e15 in existing maximal gap tables
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REFERENCES
| R. K. Guy: Unsolved problems in number theory, 2nd ed., Springer-Verlag,1994; Sections A8, A 9.
Paulo Ribenboim: The little book of big primes, Springer-Verlag,1991; 142ff
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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EXAMPLE
| a(12) = 2 because between p(12)= 37 and 37+sqrt(37) = 43.08 there are two primes: 41 and 43
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CROSSREFS
| Cf. A030296.
Sequence in context: A105551 A073772 A164562 * A070000 A037803 A184318
Adjacent sequences: A058185 A058186 A058187 * A058189 A058190 A058191
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KEYWORD
| nonn
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AUTHOR
| Adam Kertesz (adamkertesz(AT)worldnet.att.net), Dec 04 2000
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