A053980 Engel expansion of zeta(3) = 1.20206... .

1, 5, 98, 127, 923, 5474, 16490, 25355, 37910, 85150, 1033216, 2290644, 7844861, 11170684, 18884358, 21481832, 35060787, 52399788, 201059261, 261533994, 9939708446, 211698940106, 3030068839686, 4326424644987, 6082687570463

Offset

1,2

Comments

Cf. A006784 for definition of Engel expansion.

References

F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.

P. Erdős and Jeffrey Shallit, New bounds on the length of finite Pierce and Engel series, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.

Index entries for sequences related to Engel expansions

Mathematica

EngelExp[ A_, n_ ] := Join[ Array[ 1&, Floor[ A ] ], First@Transpose@NestList[ {Ceiling[ 1/Expand[ #[[ 1 ] ]#[[ 2 ] ]-1 ] ], Expand[ #[[ 1 ] ]#[[ 2 ] ]-1 ]}&, {Ceiling[ 1/(A-Floor[ A ]) ], A-Floor[ A ]}, n-1 ] ]

Crossrefs

Cf. A006784, A028254, A028257.

Cf. A002117, A067912.

Sequence in context: A202516 A062538 A350874 * A215299 A088995 A093749

Adjacent sequences: A053977 A053978 A053979 * A053981 A053982 A053983

Keyword

nonn,easy,nice

Author

Jeppe Stig Nielsen, Apr 02 2000

Extensions

More terms and additional comments from Mitch Harris, Jan 15 2001

Status

approved