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Search: id:A159835
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| A159835 |
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Engel expansion of hz = limit_{k->infinity} 1 +k -Sum_{j=-k..k} exp(-2^j). |
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1
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| 1, 4, 4, 4, 4, 6, 11, 11, 11, 14, 61, 266, 1006, 1030, 1261, 6264, 7583, 7979, 7986, 12386, 80041, 87434, 130927, 270073, 1653819, 1715177, 1973657, 3483485, 12346987, 17531499, 21237674, 84101406, 95403456, 664784809, 14591838849
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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hz = 1.33274738243289922500860109837389970441674398225984453657972 ...
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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Eric Weisstein's World of Mathematics, Engel Expansion
Index entries for sequences related to Engel expansions
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MAPLE
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hz:= limit (1+k -sum (exp (-2^j), j=-k..k), k=infinity): engel:= (r, n)-> `if` (n=0 or r=0, NULL, [ceil(1/r), engel (r*ceil(1/r)-1, n-1)][]): Digits:=120: engel (evalf(hz), 39);
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CROSSREFS
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Cf. A158468 (decimal expansion), A158469 (continued fraction).
Sequence in context: A111655 A113646 A106325 this_sequence A047210 A120327 A056629
Adjacent sequences: A159832 A159833 A159834 this_sequence A159836 A159837 A159838
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 23 2009
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