|
| |
|
|
A091590
|
|
Number of terms in the simple continued fraction for the 10^n-th harmonic number, H_n = sum_{k=1 to n} (1/k).
|
|
0
| | |
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Conjecture: lim n -> infinity, a(n)/10^n -> C = 12*ln(2)/Pi^2 = 0.842... - Benoit Cloitre (benoit7848c(AT)orange.fr), May 04 2002
|
|
|
REFERENCES
| S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 156.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Harmonic Number
|
|
|
MATHEMATICA
| s = 0; k = 1; Do[ While[s = s + 1/k; k < 10^n, k++ ]; Print[ Length[ ContinuedFraction[s]]]; k++, {n, 0, 6}]
|
|
|
CROSSREFS
| Cf. A055573. n-th harmonic number H(m) = A001008(n)/A002805(n).
Sequence in context: A167859 A113357 A030992 * A087487 A178368 A152279
Adjacent sequences: A091587 A091588 A091589 * A091591 A091592 A091593
|
|
|
KEYWORD
| cofr,hard,nonn
|
|
|
AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 22 2004
|
|
|
EXTENSIONS
| Corrected and extended by Eric Weisstein (eric(AT)weisstein.com), Jan 23, 2004
|
| |
|
|
