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A002392
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Decimal expansion of natural logarithm of 10.
(Formerly M0394 N0151)
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13
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2, 3, 0, 2, 5, 8, 5, 0, 9, 2, 9, 9, 4, 0, 4, 5, 6, 8, 4, 0, 1, 7, 9, 9, 1, 4, 5, 4, 6, 8, 4, 3, 6, 4, 2, 0, 7, 6, 0, 1, 1, 0, 1, 4, 8, 8, 6, 2, 8, 7, 7, 2, 9, 7, 6, 0, 3, 3, 3, 2, 7, 9, 0, 0, 9, 6, 7, 5, 7
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OFFSET
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1,1
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COMMENTS
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10 ln 10 ~ 23.0258509299... appears in Bakir Farhi's paper. Abstract: It is well known since A. J. Kempner's work that the series of the reciprocals of the positive integers whose the decimal representation does not contain any digit 9, is convergent. This result was extended by F. Irwin and others to deal with the series of the reciprocals of the positive integers whose the decimal representation contains only a limited quantity of each digit of a given nonempty set of digits. Actually, such series are known to be all convergent. Here, letting S^{(r)} (r in N}) denote the series of the reciprocal of the positive integers whose the decimal representation contains the digit 9 exactly r times, the impressive obtained result is that S^{(r)} tends to 10 log{10} as r tends to infinity! - Jonathan Vos Post, Jul 23 2008
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REFERENCES
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A. J. Kempner, A curious convergent series, Amer. Math. Monthly 23(1914)48-50.
W. E. Mansell, Tables of Natural and Common Logarithms. Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, 1964, p. 2.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Uhler, Horace S.; Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7 and 17. Proc. Nat. Acad. Sci. U. S. A. 26, (1940). 205-212.
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..20000
Bakir Farhi, A curious result related to Kempner's series, Jul 22, 2008.
_Simon Plouffe_, log(10) the natural logatithm of 10 to 2000 digits
_Simon Plouffe_, Plouffe's Inverter, The natural logarithm of 10 to 2000 digits
Eric Weisstein's World of Mathematics, Natural Logarithm of 10
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EXAMPLE
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2.302585092994045684017991454684364207601101488628772976033327900967572...
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PROG
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(PARI) { default(realprecision, 20080); x=log(10); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002392.txt", n, " ", d)); } [From Harry J. Smith, Apr 16 2009]
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CROSSREFS
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Cf. A016738 (continued fraction).
Sequence in context: A024307 A219864 A194745 * A002708 A167925 A209927
Adjacent sequences: A002389 A002390 A002391 * A002393 A002394 A002395
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KEYWORD
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cons,nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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