Search: id:A159835
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%I A159835
%S A159835 1,4,4,4,4,6,11,11,11,14,61,266,1006,1030,1261,6264,7583,7979,7986,
%T A159835 12386,80041,87434,130927,270073,1653819,1715177,1973657,3483485,
%U A159835 12346987,17531499,21237674,84101406,95403456,664784809,14591838849
%N A159835 Engel expansion of hz = limit_{k->infinity} 1 +k -Sum_{j=-k..k} exp(-2^j).
%C A159835 hz = 1.33274738243289922500860109837389970441674398225984453657972 ...
%C A159835 Cf. A006784 for definition of Engel expansion.
%D A159835 F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 
               52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 
               1913, pp. 190-191.
%D A159835 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.
%H A159835 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EngelExpansion.html">Engel Expansion</a>
%H A159835 <a href="Sindx_El.html#Engel">Index entries for sequences related to 
               Engel expansions</a>
%p A159835 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);
%Y A159835 Cf. A158468 (decimal expansion), A158469 (continued fraction).
%Y A159835 Sequence in context: A111655 A113646 A106325 this_sequence A047210 A120327 
               A056629
%Y A159835 Adjacent sequences: A159832 A159833 A159834 this_sequence A159836 A159837 
               A159838
%K A159835 easy,nice,nonn
%O A159835 1,2
%A A159835 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 23 2009

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