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A108954
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a(n) = Pi(2n) - Pi(n).
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5
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1, 1, 1, 2, 1, 2, 2, 2, 3, 4, 3, 4, 3, 3, 4, 5, 4, 4, 4, 4, 5, 6, 5, 6, 6, 6, 7, 7, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 9, 10, 9, 9, 10, 10, 9, 9, 10, 10, 11, 12, 11, 12, 13, 13, 14, 14, 13, 13, 12, 12, 12, 13, 13, 14, 13, 13, 14, 15, 14, 14, 13, 13, 14, 15, 15, 15, 15, 15, 15, 16, 15, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) < log(4)*n/log(n) < 7*n/(5*log(n)) for n > 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2008
Bertrand's postulate is equivalent to the formula a(n) => 1 for all positive integers n. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 30 2008
Number of distinct prime factors > n of binomial(2*n,n). - T. D. Noe, Aug 18 2011
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REFERENCES
| F. Irschebeck, Einladung zur Zahlentheorie, BI Wissenschaftsverlag 1992, p. 40
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
Tsutomu Hashimoto, On a certain relation between Legendre's conjecture and Bertrand's postulate
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FORMULA
| Pi(x) = number of prime numbers less than or equal to x.
For n > 1, a(n) = A060715(n). - David Wasserman (wasserma(AT)spawar.navy.mil), Nov 04 2005
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MATHEMATICA
| Table[Length[Select[Transpose[FactorInteger[Binomial[2 n, n]]][[1]], # > n &]], {n, 100}] (* T. D. Noe, Aug 18 2011 *)
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PROG
| (PARI) g(n) = for(x=1, n, y=primepi(2*x)-primepi(x); print1(y", "))
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CROSSREFS
| a(n)=A000720(2*n)-A000720(n).
Cf. A000720, A060715.
Cf. A067434 (number of prime factors in binomial(2*n,n)), A193990.
Sequence in context: A114920 A030361 A060715 * A123920 A029170 A079526
Adjacent sequences: A108951 A108952 A108953 * A108955 A108956 A108957
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Jul 22 2005
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