A059195 Engel expansion of log(Pi) = 1.14473... .

1, 7, 77, 107, 150, 167, 7091, 27852, 31790, 34069, 327724, 416403, 4669290, 20206510, 2218014305, 4524826037, 4576058224, 5496581959, 15869888136, 91151928112, 104430320239, 202761572952, 218933128153, 937032410920, 1044739832405, 15262515810234

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

Crossrefs

Cf. A053510.

Sequence in context: A166169 A284068 A153688 * A139264 A045642 A292457

Adjacent sequences: A059192 A059193 A059194 * A059196 A059197 A059198

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved