A059179 Engel expansion of 3^(1/3) = 1.44225.

1, 3, 4, 4, 5, 8, 9, 14, 63, 91, 132, 605, 753, 993, 17297, 26120, 28227, 43466, 123132, 3551445, 7243732, 13958201, 41249856, 194184556, 3261328035, 13339681270, 18470226192, 23831447862, 25356135862

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[3^(1/3), 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *)

Crossrefs

Sequence in context: A111914 A051665 A028263 * A384318 A279678 A381552

Adjacent sequences: A059176 A059177 A059178 * A059180 A059181 A059182

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved