Search: id:A004080
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%I A004080
%S A004080 0,1,4,11,31,83,227,616,1674,4550,12367,33617,91380,248397,675214,
%T A004080 1835421,4989191,13562027,36865412,100210581,272400600,740461601,
%U A004080 2012783315,5471312310,14872568831,40427833596,109894245429,298723530401,
               812014744422
%N A004080 Least k such that H(k) >= n, where H(k) is the harmonic number sum_{i=1..k} 
               1/i.
%D A004080 J. V. Baxley, Euler's constant, Taylor's formula and slowly converging 
               series, Math. Mag., 65 (1992), 302-313.
%D A004080 R. P. Boas, Jr. and J. W. Wrench, Jr., Partial sums of the harmonic series, 
               Amer. Math. Monthly, 78 (1971), 864-870.
%D A004080 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]
%D A004080 W. Sierpi\'{n}ski, Sur les decompositions de nombres rationnels, Oeuvres 
               Choisies, Acad\'{e}mie Polonaise des Sciences, Warsaw, Poland, 1974, 
               p. 181.
%D A004080 N. J. A. Sloane, Illustration for sequence M4299 (=A007340) in The Encyclopedia 
               of Integer Sequences (with S. Plouffe), Academic Press, 1995.
%H A004080 T. D. Noe, <a href="b004080.txt">Table of n, a(n) for n=0..100</a> (using 
               Hickerson's formula in A002387)
%H A004080 J. Derbyshire, <a href="http://olimu.com/Notes/Rain.htm">Rainfall Records</
               a>
%H A004080 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HarmonicSeries.html">Link to a section of The World of Mathematics.</
               a>
%H A004080 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HarmonicNumber.html">Harmonic Number</a>
%H A004080 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               High-WaterMark.html">High-Water Mark</a>
%F A004080 The quotient of two successive terms of this sequence has exp(1) for 
               limit. - Sebastien Dumortier (sdumortier(AT)ac-limoges.fr), Jun 29 
               2005
%F A004080 a(n) ~ exp(n-gamma) [From Charles R Greathouse IV Mar 10 2009]
%e A004080 a(2)=4 because 1/1+1/2+1/3+1/4>2
%o A004080 (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
%Y A004080 Apart from first two terms, same as A002387.
%Y A004080 Sequence in context: A090327 A104743 A165993 this_sequence A027115 A077995 
               A076730
%Y A004080 Adjacent sequences: A004077 A004078 A004079 this_sequence A004081 A004082 
               A004083
%K A004080 nonn,nice
%O A004080 0,3
%A A004080 N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu)
%E A004080 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.
%E A004080 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Apr 19 2003
%E A004080 More terms from Sebastien Dumortier (sdumortier(AT)ac-limoges.fr), Jun 
               29 2005
%E A004080 a(27) from Thomas Gettys (tpgettys(AT)comcast.net), Dec 05 2006
%E A004080 a(28) from Thomas Gettys (tpgettys(AT)comcast.net), Jan 21 2007

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