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Search: id:A028259
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| A028259 |
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Engel expansion of the golden ratio, (1+sqrt(5))/2 = 1.61803. |
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3
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| 1, 2, 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; listen)
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OFFSET
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1,2
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COMMENT
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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.
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
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T. D. Noe, Table of n, a(n) for n=1..300
Index entries for sequences related to Engel expansions
Eric Weisstein's World of Mathematics, Engel Expansion
Eric Weisstein's World of Mathematics, Golden Ratio
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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 ]}&, {Ceiling[ 1/(A-Floor[ A ]) ], A-Floor[ A ]}, n-1 ] ]
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CROSSREFS
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Sequence in context: A070911 A113240 A098376 this_sequence A027010 A038191 A087128
Adjacent sequences: A028256 A028257 A028258 this_sequence A028260 A028261 A028262
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Naoki Sato (naoki(AT)math.toronto.edu)
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 16 2001
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