A059182 Engel expansion of log(10) = 2.30259...

1, 1, 4, 5, 20, 30, 48, 74, 265, 818, 897, 2027, 5107, 6846, 13049, 236586, 364437, 643493, 1144424, 7294777, 49484843, 51161394, 76008087, 202870914, 391981014, 11731070977, 79069971960, 415100034571, 1212266245583

Offset

1,3

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.

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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

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[10], 7!], 50] (* modified by G. C. Greubel, Dec 26 2016 *)

Crossrefs

Cf. A002392.

Sequence in context: A182584 A358581 A240860 * A027958 A293942 A064670

Adjacent sequences: A059179 A059180 A059181 * A059183 A059184 A059185

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved