A139001 Partial sums of A055573 = number of terms in continued fraction of H(n)=sum(1/k,k=1..n).

1, 3, 6, 8, 13, 17, 23, 30, 40, 48, 55, 65, 80, 89, 98, 115, 133, 144, 164, 180, 198, 216, 239, 258, 282, 307, 331, 357, 386, 407, 431, 454, 480, 505, 537, 571, 604, 630, 654, 685, 717, 748, 784, 820, 859, 891, 925, 967, 1014, 1058, 1104, 1139, 1179, 1227, 1270

Offset: 1

Author

M. F. Hasler, May 31 2008

Keywords

• nonn

Comments

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.

Links

• M. F. Hasler, Table of n, a(n) for n = 1..500

Crossrefs

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

Programs

PARI

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

Formula

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