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A002392 Decimal expansion of natural logarithm of 10.
(Formerly M0394 N0151)
21
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

10 log 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 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 decimal representation contains only a limited quantity of each digit of a given nonempty set of digits. Actually, such series are all known to be convergent. Here, letting S^{(r)} (r in N}) denote the series of the reciprocals of the positive integers whose decimal representation contains the digit 9 exactly r times, the impressive result obtained is that S^{(r)} tends to 10 log{10} as r tends to infinity! - Jonathan Vos Post, Jul 23 2008

REFERENCES

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).

LINKS

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.

A. J. Kempner, A curious convergent series, Amer. Math. Monthly 23(1914)48-50.

Simon Plouffe, log(10) the natural logarithm of 10 to 2000 digits

Simon Plouffe, Plouffe's Inverter, The natural logarithm of 10 to 2000 digits

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.

Eric Weisstein's World of Mathematics, Natural Logarithm of 10

EXAMPLE

2.302585092994045684017991454684364207601101488628772976033327900967572...

MATHEMATICA

RealDigits[Log[10], 10, 120][[1]] (* Harvey P. Dale, Nov 23 2013 *)

PROG

(PARI) { default(realprecision, 20080); x=log(10); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002392.txt", n, " ", d)); } \\ Harry J. Smith, Apr 16 2009

CROSSREFS

Cf. A016738 (continued fraction).

Sequence in context: A219864 A194745 A248342 * A002708 A167925 A209927

Adjacent sequences:  A002389 A002390 A002391 * A002393 A002394 A002395

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 21 20:27 EST 2014. Contains 252326 sequences.