A059194 Engel expansion of 1/e^2 = 0.135335... .

8, 13, 14, 21, 87, 92, 119, 444, 472, 473, 548, 5380, 7995, 100393, 589494, 2034930, 12322338, 21633910, 55986423, 164342975, 6502609245, 22562439736, 26621735244, 39286977900, 576511092268, 892451075829, 1050206120774, 2228669763793, 3336969029043

Offset

1,1

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 and T. D. Noe, Table of n, a(n) for n = 1..1000 [Terms 1 to 300 computed by T. D. Noe; Terms 301 to 1000 computed by G. C. Greubel, Dec 28 2016]

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[1/E^2, 7!], 100] (* Modified by G. C. Greubel, Dec 28 2016 *)

Crossrefs

Cf. A092553.

Sequence in context: A128662 A133192 A063684 * A253775 A168137 A252458

Adjacent sequences: A059191 A059192 A059193 * A059195 A059196 A059197

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved