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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. 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

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

Mitch Harris

STATUS

approved

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