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A059195
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Engel expansion of log(Pi) = 1.14473... .
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2
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1, 7, 77, 107, 150, 167, 7091, 27852, 31790, 34069, 327724, 416403, 4669290, 20206510, 2218014305, 4524826037, 4576058224, 5496581959, 15869888136, 91151928112, 104430320239, 202761572952, 218933128153, 937032410920, 1044739832405, 15262515810234
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OFFSET
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1,2
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COMMENTS
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Cf. A006784 for definition of Engel expansion.
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REFERENCES
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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
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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.
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MATHEMATICA
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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[Pi], 7!], 100] (* Modified by G. C. Greubel, Dec 28 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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