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A059176
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Engel expansion of sqrt(5) = 2.23607.
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1
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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; internal format)
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OFFSET
| 1,3
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COMMENTS
| Cf. A006784 for definition of Engel expansion
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REFERENCES
| F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.
P. Erdos and J. O. 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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LINKS
| Index entries for sequences related to Engel expansions
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MATHEMATICA
| EngelExp[ A_, n_ ] := Join[ Array[ 1&, Floor[ A ] ], First@Transpose@NestList[ {Ceiling[ 1/Expand[ #[ [ 1 ] ]#[ [ 2 ] ]-1 ] ], Expand[ #[ [ 1 ] ]#[ [ 2 ] ]-1 ]}&, {Ceiling[ 1/(A-Floor[ A ]) ], A-Floor[ A ]}, n-1 ] ]
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CROSSREFS
| Cf. A028259. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 30 2009]
Sequence in context: A047436 A061437 A067245 * A030356 A138937 A099330
Adjacent sequences: A059173 A059174 A059175 * A059177 A059178 A059179
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu)
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