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Search: id:A004080
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| A004080 |
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Least k such that H(k) >= n, where H(k) is the harmonic number sum_{i=1..k} 1/i. |
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+0
22
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| 0, 1, 4, 11, 31, 83, 227, 616, 1674, 4550, 12367, 33617, 91380, 248397, 675214, 1835421, 4989191, 13562027, 36865412, 100210581, 272400600, 740461601, 2012783315, 5471312310, 14872568831, 40427833596, 109894245429, 298723530401, 812014744422
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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J. V. Baxley, Euler's constant, Taylor's formula and slowly converging series, Math. Mag., 65 (1992), 302-313.
R. P. Boas, Jr. and J. W. Wrench, Jr., Partial sums of the harmonic series, Amer. Math. Monthly, 78 (1971), 864-870.
Bruno Rizzi and Cristina Scagliarini: I numeri armonici. Periodico di matematiche, "Mathesis", pp. 17-58, 1986, numbers 1-2 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 05 2009]
W. Sierpi\'{n}ski, Sur les decompositions de nombres rationnels, Oeuvres Choisies, Acad\'{e}mie Polonaise des Sciences, Warsaw, Poland, 1974, p. 181.
N. J. A. Sloane, Illustration for sequence M4299 (=A007340) in The Encyclopedia of Integer Sequences (with S. Plouffe), Academic Press, 1995.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100 (using Hickerson's formula in A002387)
J. Derbyshire, Rainfall Records
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, High-Water Mark
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FORMULA
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The quotient of two successive terms of this sequence has exp(1) for limit. - Sebastien Dumortier (sdumortier(AT)ac-limoges.fr), Jun 29 2005
a(n) ~ exp(n-gamma) [From Charles R Greathouse IV Mar 10 2009]
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EXAMPLE
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a(2)=4 because 1/1+1/2+1/3+1/4>2
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PROGRAM
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(PARI) gp > t=0; n=0; for(i=1, 10^20, t+=1./i; if(t>=n, print(i, " ", t); n++)) - Thomas Gettys (tpgettys(AT)comcast.net), Jan 21 2007
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CROSSREFS
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Apart from first two terms, same as A002387.
Sequence in context: A090327 A104743 A165993 this_sequence A027115 A077995 A076730
Adjacent sequences: A004077 A004078 A004079 this_sequence A004081 A004082 A004083
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Terms for n >= 13 computed by Eric Weisstein (eric(AT)weisstein.com). Corrected by Jim Buddenhagen (jbuddenh(AT)gmail.com) and Eric W. Weisstein (eric(AT)weisstein.com), Feb 18 2001.
Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Apr 19 2003
More terms from Sebastien Dumortier (sdumortier(AT)ac-limoges.fr), Jun 29 2005
a(27) from Thomas Gettys (tpgettys(AT)comcast.net), Dec 05 2006
a(28) from Thomas Gettys (tpgettys(AT)comcast.net), Jan 21 2007
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