A059178 Engel expansion of 2^(1/3) = 1.25992.

1, 4, 26, 32, 58, 1361, 4767, 22303, 134563, 188609, 282816, 979804, 1272032, 1330628, 3719474, 5039143, 12531368, 435451235, 5391276884, 6140156718, 24140682996, 30267765913, 56443830660, 176797839116, 645251112512

Offset: 1

Author

Mitch Harris

Keywords

• nonn
• easy
• nice

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

Crossrefs

Cf. A002580.

Programs

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[2^(1/3), 7!], 10] (* modified by G. C. Greubel, Dec 26 2016 *)