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A159835
Engel expansion of hz = limit_{k -> infinity} 1 + k - Sum_{j = -k..k} exp(-2^j).
2
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, 84103203, 195088616, 725688944, 2813572082, 3138084145, 10870485195
OFFSET
1,2
COMMENTS
Cf. A006784 for definition of Engel expansion.
REFERENCES
F. Engel, Entwicklung der Zahlen nach Stammbrüchen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmänner in Marburg, 1913, pp. 190-191.
LINKS
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.
Eric Weisstein's World of Mathematics, Engel Expansion
Wikipedia, Engel Expansion
EXAMPLE
hz = 1.3327473824328992250086010983738997044167439822598445365797 ...
MAPLE
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:=300:
engel(evalf(hz), 39);
CROSSREFS
Cf. A158468 (decimal expansion), A158469 (continued fraction).
Sequence in context: A175961 A113646 A106325 * A240835 A047210 A360915
KEYWORD
easy,nice,nonn
AUTHOR
Alois P. Heinz, Apr 23 2009
EXTENSIONS
Some terms corrected by Alois P. Heinz, Nov 22 2020
STATUS
approved