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 A059176 Engel expansion of sqrt(5) = 2.23606... 2
 1, 1, 5, 6, 13, 16, 16, 38, 48, 58, 104, 177, 263, 332, 389, 4102, 4575, 5081, 9962, 18316, 86613, 233239, 342534, 964372, 1452850, 7037119, 7339713, 8270361, 12855437, 15900982, 19211148, 1365302354, 1565752087, 1731612283 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Simon Plouffe, Table of n, a(n) for n = 1..883 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. ErdÅ‘s 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. 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[Sqrt[5], 7!], 50] (* modified by G. C. Greubel, Dec 26 2016 *) CROSSREFS Cf. A002163. Cf. A028259. - R. J. Mathar, Jan 30 2009 Sequence in context: A047436 A061437 A067245 * A219978 A326657 A303139 Adjacent sequences:  A059173 A059174 A059175 * A059177 A059178 A059179 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified October 17 22:05 EDT 2019. Contains 328134 sequences. (Running on oeis4.)