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A059197
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Engel expansion of Pi^e = 22.4592.
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1
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 8, 17, 111, 236, 419, 2475, 3741, 4123, 5563, 5622, 18000, 33641, 42744, 130605, 696987, 975174, 1034590, 2806140, 14026897, 14137435, 65788323, 73121589, 229261119
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OFFSET
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1,23
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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[Pi^E, 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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