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A035250
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Number of primes between n and 2n (inclusive).
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18
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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
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OFFSET
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1,2
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COMMENTS
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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, Jan 01 2007
a(n) = A000720(2*n) - A000720(n-1); a(n) <= A179211(n). [From Reinhard Zumkeller, Jul 05 2010]
a(A059316(n)) = n and a(m) <> n for m < A059316(n). [Reinhard Zumkeller, Jan 08 2012]
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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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FORMULA
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a(n) = sum(A010051(k): k=n..2*n). [Reinhard Zumkeller, Jan 08 2012]
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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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MATHEMATICA
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f[n_] := PrimePi[ 2n] - PrimePi[n - 1]; Array[f, 76] (* Robert G. Wilson v, Dec 23 2012 *)
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PROG
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(Haskell)
a035250 n = sum $ map a010051 [n..2*n] -- Reinhard Zumkeller, Jan 08 2012
(MAGMA) [#PrimesInInterval(n, 2*n): n in [1..80]]; // Bruno Berselli, Sep 05 2012
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CROSSREFS
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Cf. A073837, A073838, A099802. [From Reinhard Zumkeller, Jul 05 2010]
Cf. A060715.
Sequence in context: A125973 A189172 A001031 * A165054 A067743 A029230
Adjacent sequences: A035247 A035248 A035249 * A035251 A035252 A035253
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KEYWORD
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nonn
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AUTHOR
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Erich Friedman
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STATUS
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approved
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