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Search: id:A059180
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| A059180 |
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Engel expansion of ln(2) = 0.693147. |
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+0
2
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| 2, 3, 7, 9, 104, 510, 1413, 2386, 40447, 87110, 124975, 1565154, 1766158, 2440919, 2637001, 9192874, 24998746, 73973182, 88828340, 432049320, 470421590, 477600793, 3313014448, 4571423959, 28839435286, 40818751774
(list; graph; listen)
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OFFSET
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1,1
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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, Natural Logarithm of 2
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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: A107861 A109800 A152136 this_sequence A051637 A051471 A047531
Adjacent sequences: A059177 A059178 A059179 this_sequence A059181 A059182 A059183
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu)
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