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

Author

Mitch Harris

Keywords

• nonn
• easy
• nice

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

Crossrefs

Cf. A039661.

Programs

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 *)