A059199 Engel expansion of e^gamma (gamma is the Euler-Mascheroni constant A001620) = 1.78107.

1, 2, 2, 9, 9, 15, 84, 256, 278, 819, 1734, 6500, 10004, 20116, 26612, 31762827, 181599789, 981641086, 1698644383, 1987894743, 5557385559, 11998593788, 12646182115, 70932754473, 106473857370, 527311590750

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

Crossrefs

Cf. A073004.

Sequence in context: A056856 A133920 A229594 * A010765 A193477 A193726

Adjacent sequences: A059196 A059197 A059198 * A059200 A059201 A059202

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved