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Search: id:A035250
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| A035250 |
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Number of primes between n and 2n (inclusive). |
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+0
11
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| 1, 2, 2, 2, 2, 2, 3, 2, 3, 4, 4, 4, 4, 3, 4, 5, 5, 4, 5, 4, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 7, 7, 8, 8, 9, 10, 9, 9, 10, 10, 10, 10, 9, 10, 10, 10, 9, 10, 10, 11, 12, 12, 12, 13, 13, 14, 14, 14, 13, 13, 12, 12, 13, 13, 14, 14, 13, 14, 15, 15, 14, 14, 13, 14, 15, 15, 15, 16, 15, 15, 16, 16
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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By Bertrand's Postulate (proved by Chebyshev), there is always a prime between n and 2n, i.e. a(n) is positive for all n.
The smallest and largest primes between n and 2n inclusive are A007918 and A060308 respectively. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 01 2007
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REFERENCES
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Aigner, M. and Ziegler, G. Proofs from The Book (2nd edition). Springer-Verlag, 2001.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
International Mathematics Olympiad, Proof of Bertrand's Postulate
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EXAMPLE
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The primes between n = 13 and 2n = 26, inclusive, are 13, 17, 19, 23; so a(13) = 4.
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CROSSREFS
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Sequence in context: A120676 A125973 A001031 this_sequence A067743 A029230 A084294
Adjacent sequences: A035247 A035248 A035249 this_sequence A035251 A035252 A035253
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KEYWORD
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nonn
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AUTHOR
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Erich Friedman (erich.friedman(AT)stetson.edu)
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