A113123 Numerator of next-best approximation to harmonic numbers. a(n) = Numerator of (A055573(n)-1)th convergent of n-th harmonic number, Sum_{k=1..n} 1/k.

0, 1, 2, 2, 16, 22, 70, 106, 1836, 2639, 14281, 21167, 167857, 87932, 169452, 923889, 3590229, 950596, 40366604, 23213361, 517630, 1391957, 160363133, 222528683, 10125035246, 4324958013, 81828906108, 71315450571, 4320297286472

Offset: 1

Author

Leroy Quet, Oct 14 2005

Keywords

• easy
• frac
• nonn

Comments

A100398 gives terms of continued fractions of harmonic numbers.

For n >= 2, a(n) = the denominator of the ratio equal to the continued fraction made by reversing the order of the terms of the continued fraction of the n-th harmonic number. (The numerator of this ratio is the numerator of the n-th harmonic number, A001008(n).) - Leroy Quet, Dec 24 2006

Examples

			H(6) = 49/20 = 2 +1/(2 +1/(4 +1/2)), so a(6) = numerator of 2 +1/(2 +1/4) = 22/9.
		

Crossrefs

Cf. A100398, A055573, A113124.

Extensions

More terms from Joshua Zucker, May 08 2006