A100398 Array where n-th row (of A055573(n) terms) is the continued fraction terms for the n-th harmonic number, sum{ k=1 to n} 1/k.

1, 1, 2, 1, 1, 5, 2, 12, 2, 3, 1, 1, 8, 2, 2, 4, 2, 2, 1, 1, 2, 5, 5, 2, 1, 2, 1, 1, 5, 7, 2, 1, 4, 1, 5, 1, 1, 7, 1, 3, 2, 1, 13, 12, 1, 3, 1, 2, 3, 50, 3, 4, 6, 1, 5, 3, 9, 1, 2, 4, 1, 1, 1, 15, 4, 3, 5, 1, 1, 4, 2, 1, 3, 2, 1, 3, 1, 4, 1, 6, 3, 3, 1, 39, 3, 1, 13, 3, 13, 3, 3, 7, 43, 1, 1, 1, 17, 7, 3, 2

Offset: 1

Author

Leroy Quet, Dec 30 2004

Keywords

• nonn
• tabl

Comments

Terms corresponding to H(n) (i.e. the n-th row) end at index A139001(n)=sum(i=1..n,A055573(n)) - M. F. Hasler, May 31 2008

Examples

			Since the 3rd harmonic number is 11/6 = 1 +1/(1 +1/5), the 3rd row is 1,1,5.
		

Links

• M. F. Hasler, Table of n, a(n) for n=1..105013.
• Eric Weisstein's World of Mathematics, Harmonic Number
• Eric Weisstein's World of Mathematics, Continued Fraction

Crossrefs

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

Cf. A055573, A058027, A110020, A112286, A112287.

Programs

Mathematica

Flatten[Table[ContinuedFraction[HarmonicNumber[n]], {n, 16}]] (* Ray Chandler, Sep 17 2005 *)

PARI

c=0;h=0;for(n=1,500,for(i=1,#t=contfrac(h+=1/n),write("b100398.txt",c++," ",t[i]))) \\ M. F. Hasler, May 31 2008

Extensions

Extended by Ray Chandler, Sep 17 2005