A059197 Engel expansion of Pi^e = 22.4592.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 8, 17, 111, 236, 419, 2475, 3741, 4123, 5563, 5622, 18000, 33641, 42744, 130605, 696987, 975174, 1034590, 2806140, 14026897, 14137435, 65788323, 73121589, 229261119

Offset

1,23

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..1022

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[Pi^E, 7!], 100] (* Modified by G. C. Greubel, Dec 28 2016 *)

Crossrefs

Cf. A059850.

Sequence in context: A327327 A370640 A328976 * A049974 A049972 A027376

Adjacent sequences: A059194 A059195 A059196 * A059198 A059199 A059200

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved