%I A059180
%S A059180 2,3,7,9,104,510,1413,2386,40447,87110,124975,1565154,1766158,2440919,
%T A059180 2637001,9192874,24998746,73973182,88828340,432049320,470421590,
%U A059180 477600793,3313014448,4571423959,28839435286,40818751774
%N A059180 Engel expansion of ln(2) = 0.693147.
%C A059180 Cf. A006784 for definition of Engel expansion
%D A059180 F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 
               52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 
               1913, pp. 190-191.
%D A059180 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 A059180 T. D. Noe, <a href="b059180.txt">Table of n, a(n) for n=1..300</a>
%H A059180 <a href="Sindx_El.html#Engel">Index entries for sequences related to 
               Engel expansions</a>
%H A059180 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EngelExpansion.html">Engel Expansion</a>
%H A059180 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NaturalLogarithmof2.html">Natural Logarithm of 2</a>
%t A059180 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 
               ] ]
%Y A059180 Sequence in context: A107861 A109800 A152136 this_sequence A051637 A051471 
               A047531
%Y A059180 Adjacent sequences: A059177 A059178 A059179 this_sequence A059181 A059182 
               A059183
%K A059180 nonn,easy,nice
%O A059180 1,1
%A A059180 Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu)