A059177 Engel expansion of sqrt(10) = 3.16227...

1, 1, 1, 7, 8, 12, 20, 86, 94, 118, 160, 179, 287, 315, 22588, 49419, 66011, 80779, 651661, 1078390, 1093865, 4254100, 27153191, 108815387, 220864645, 798937058, 992296124, 2196903274, 17524412379, 22828187385

Offset

1,4

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[Sqrt[10], 7!], 10] (* modified by G. C. Greubel, Dec 26 2016 *)

Crossrefs

Cf. A010467.

Sequence in context: A024706 A050901 A105832 * A065729 A156605 A343298

Adjacent sequences: A059174 A059175 A059176 * A059178 A059179 A059180

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved