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A006879
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Number of primes with n digits.
(Formerly M3577)
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18
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0, 4, 21, 143, 1061, 8363, 68906, 586081, 5096876, 45086079, 404204977, 3663002302, 33489857205, 308457624821, 2858876213963, 26639628671867, 249393770611256, 2344318816620308, 22116397130086627, 209317712988603747, 1986761935284574233, 18906449883457813088, 180340017203297174362
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OFFSET
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0,2
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COMMENTS
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Also, the number of primes between 10^(n-1) and 10^n. - Cino Hilliard (hillcino368(AT)hotmail.com), May 31 2008 (Corrected by Jon Schoenfield, Nov 29 2008)
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 21, pp 8, Ellipses, Paris 2008.
C. T. Long, Elementary Introduction to Number Theory. Prentice-Hall, Englewood Cliffs, NJ, 1987, p. 77.
P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 179.
D. Shanks, Solved and Unsolved Problems in Number Theory. Chelsea, NY, 2nd edition, 1978, p. 15.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 0..24
C. K. Caldwell, How Many Primes Are There?
Cino Hilliard Count,Sum primes in a range Win32 Gcc+Gmp.
Index entries for sequences related to numbers of primes in various ranges
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FORMULA
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a(n) = pi(10^n)-pi(10^(n-1)) where pi(10^(-1)) := 0 (cf. A000720).
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EXAMPLE
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As 2,3,5 and 7 are the only primes less than 10 the term a(1) = 4.
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PROG
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(PARI) a(n)=primepi(10^n)-primepi(10^(n-1)) \\ Charles R Greathouse IV, May 03 2012
(C) See Hilliard link.
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CROSSREFS
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First differences of A006880.
Sequence in context: A120368 A053482 A158577 * A163861 A006153 A183387
Adjacent sequences: A006876 A006877 A006878 * A006880 A006881 A006882
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KEYWORD
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nonn,base,hard
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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EXTENSIONS
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11-th and 12th terms corrected by Jud McCranie and Enoch Haga; 19th term corrected and 20th term added by Paul.Zimmermann(AT)loria.fr (Paul Zimmermann).
a(21)-a(22) from Vladeta Jovovic, Nov 07 2001
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STATUS
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approved
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