A059183 Engel expansion of 1/log(2) = 1.4427...

1, 3, 4, 4, 5, 5, 5, 6, 47, 109, 935, 4763, 7821, 8895, 9889, 35798, 44347, 1146551, 7874944, 8043393, 27403243, 34058912, 58098040, 68760470, 80046897, 560099631, 611427977, 14235032003, 602865059026, 813485869378

Offset: 1

Author

Mitch Harris, May 16 2003

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. A007525 (1/log(2)).

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[1/Log[2], 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *)