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
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
Crossrefs
Cf. A002392.
Programs
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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 *)
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