This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058027 Sum of terms of continued fraction for n-th harmonic number, 1 +1/2 +1/3+.. +1/n. 7

%I

%S 1,3,7,14,15,10,16,19,26,35,72,41,38,79,83,42,59,143,68,61,70,51,50,

%T 78,74,82,130,113,111,315,235,1190,211,407,112,122,142,246,693,133,

%U 138,162,1904,243,170,539,363,210,197,518,275,502,527,316,1729,224,228,909

%N Sum of terms of continued fraction for n-th harmonic number, 1 +1/2 +1/3+.. +1/n.

%C Is anything known about the asymptotics of this sequence?

%C Comment from Benoit Cloitre, Dec 23, 2003: Should be asymptotic to D*n^(3/2) D=0.4....

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>

%e 1 + 1/2 +1/3 = 11/6 = 1 + 1/(1 + 1/5). So sum of terms of continued fraction is 1 + 1 + 5 = 7.

%t Table[Plus @@ ContinuedFraction[HarmonicNumber[n]], {n, 60}] - _Ray Chandler_, Sep 17 2005

%Y m-th harmonic number H(m) = A001008(m)/A002805(m).

%Y Cf. A055573, A100398, A110020, A112286, A112287.

%K easy,nonn

%O 1,2

%A Leroy Quet Nov 15 2000

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .