A059192 Engel expansion of log(1/gamma) (where gamma is the Euler-Mascheroni constant A001620) = 0.549539...

2, 11, 12, 13, 53, 348, 5263, 9960, 17040, 33193, 72960, 125350, 663179, 1096815, 3481893, 4802237, 7782503, 9659740, 279957736, 454935116, 460488754, 1710020367, 51367039980, 55286622194, 323648965384, 2061149370731

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. A002389.

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