A059200 Engel expansion of -log(log(2)) = 0.36651292... .

3, 11, 11, 23, 62, 66, 466, 1450, 7617, 95677, 100963, 153329, 966054, 4744661, 23899231, 25086529, 52363821, 100389201, 201892089, 261170111, 312778184, 527002514, 1235004065, 1623652949, 2309078745, 8274570969

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 Schulmänner 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. A074785.

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[Log[2]], 7!], 100] (* Modified by G. C. Greubel, Dec 28 2016 *)