A059196 Engel expansion of e^Pi = 23.14069... .

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 232, 238, 428, 1103, 3261, 6085, 15565, 20674, 43910, 177426, 193017, 1480418, 1739984, 2573921, 5238757, 14403086, 25953812, 34670065, 84077823, 258624998, 330484686

Offset

1,24

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..1023

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]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]];
EngelExp[N[E^Pi, 7!], 100] (* G. C. Greubel, Dec 28 2016 *)

Crossrefs

Cf. A039661.

Sequence in context: A135808 A320915 A298905 * A027504 A078247 A273555

Adjacent sequences: A059193 A059194 A059195 * A059197 A059198 A059199

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved