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A059183
Engel expansion of 1/log(2) = 1.4427...
1
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
1,2
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
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.
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 *)
CROSSREFS
Cf. A007525 (1/log(2)).
Sequence in context: A053405 A133196 A179841 * A262302 A182280 A196379
KEYWORD
nonn,easy,nice
AUTHOR
Mitch Harris, May 16 2003
STATUS
approved