A139001 - OEIS

A139001

Partial sums of A055573 = number of terms in continued fraction of H(n)=sum(1/k,k=1..n).

%I #5 Jul 14 2012 11:32:20

%S 1,3,6,8,13,17,23,30,40,48,55,65,80,89,98,115,133,144,164,180,198,216,

%T 239,258,282,307,331,357,386,407,431,454,480,505,537,571,604,630,654,

%U 685,717,748,784,820,859,891,925,967,1014,1058,1104,1139,1179,1227,1270

%N Partial sums of A055573 = number of terms in continued fraction of H(n)=sum(1/k,k=1..n).

%C Sequence A100398 holds the array having as n-th row the continued frac. of H(n); a(n) is the last term of the n-th row and accordingly, a(n-1)+1 is the index where the n-th row starts.

%H M. F. Hasler, <a href="/A139001/b139001.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = sum_{k=1..n} A055573(k)

%o (PARI) h=s=0;vector(100,n,s+=#contfrac(h+=1/n))

%Y Cf. A001008, A002805, A055573, A058027, A100398, A110020, A112286, A112287.

%K nonn

%O 1,2

%A _M. F. Hasler_, May 31 2008