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#23 by Susanna Cuyler at Fri Apr 13 11:24:27 EDT 2018
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#22 by Susanna Cuyler at Fri Apr 13 11:24:24 EDT 2018
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F. Engel, <a href="/A006784/a006784.pdf">Entwicklung der Zahlen nach Stammbruechen</a>, 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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approved
editing
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#21 by Alois P. Heinz at Wed Dec 28 15:41:48 EST 2016
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#20 by Alois P. Heinz at Wed Dec 28 15:40:39 EST 2016
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| NAME
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Engel expansion of e^Pi = 23.1407.14069... .
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proposed
editing
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Discussion
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| Wed Dec 28
| 15:41
| Alois P. Heinz: Digits in name were rounded.
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#19 by Michel Marcus at Wed Dec 28 15:12:56 EST 2016
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#18 by Michel Marcus at Wed Dec 28 15:12:18 EST 2016
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| CROSSREFS
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Cf. A039661.
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proposed
editing
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Discussion
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| Wed Dec 28
| 15:12
| Michel Marcus: For these sequence, i think it woul be nice if you looked for the constant in the OEIS
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#17 by G. C. Greubel at Wed Dec 28 13:18:59 EST 2016
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#16 by G. C. Greubel at Wed Dec 28 13:18:53 EST 2016
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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.
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G. C. Greubel, <a href="/A059196/b059196.txt">Table of n, a(n) for n = 1..1023</a>
P. Erdős and Jeffrey Shallit, <a href="http://www.numdam.org/item?id=JTNB_1991__3_1_43_0">New bounds on the length of finite Pierce and Engel series</a>, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.
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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[E^Pi, 7!], 100] (* G. C. Greubel, Dec 28 2016 *)
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approved
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#15 by Jon E. Schoenfield at Thu Dec 17 03:13:59 EST 2015
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#14 by Jon E. Schoenfield at Thu Dec 17 03:13:57 EST 2015
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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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P. ErdosErdős 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.
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approved
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