A110020 Final term of the simple continued fraction for H(n), where H(n) = Sum_{k=1..n} 1/k.

1, 2, 5, 12, 8, 2, 5, 7, 3, 2, 5, 4, 6, 13, 7, 2, 11, 15, 6, 2, 36, 13, 2, 6, 3, 7, 3, 4, 2, 9, 4, 2, 2, 2, 2, 2, 6, 5, 2, 3, 2, 2, 2, 2, 11, 3, 59, 8, 2, 4, 104, 103, 5, 6, 2, 2, 2, 59, 2, 2, 3, 9, 20, 4, 2, 3, 4, 3, 4, 2, 2, 2, 2, 2, 2, 4, 3, 4, 2, 3, 2, 37, 2, 49, 6, 2, 6, 10, 2, 4, 8, 15, 2, 2, 23, 2

Offset: 1

Author

Leroy Quet, Sep 03 2005

Keywords

• easy
• nonn

Examples

			H(5) = 137/60 = 2 + 1/(3 + 1/(1 + 1/(1 + 1/8))); a(5) is the final term, 8.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• 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, A100398, A112286, A112287.

Programs

Mathematica

Table[Last[ContinuedFraction[HarmonicNumber[n]]], {n, 100}] (* Ray Chandler, Sep 17 2005 *)

Extensions

Extended by Ray Chandler, Sep 17 2005