%I A028257
%S A028257 1,2,3,3,6,17,23,25,27,73,84,201,750,24981,46882,119318,
%T A028257 121154,242807,276226,3009377,3383197,37871208,45930966,
%U A028257 261728403,281868388,3021299588,3230725884,13646315477
%N A028257 Engel expansion of sqrt(3).
%H A028257 T. D. Noe, <a href="b028257.txt">Table of n, a(n) for n=1..300</a>
%H A028257 Naoki Sato, <a href="http://www.math.toronto.edu/~naoki/">Home page</
               a>
%H A028257 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EngelExpansion.html">Engel Expansion</a>
%H A028257 <a href="Sindx_Ed.html#Egypt">Index entries for sequences related to 
               Egyptian fractions</a>
%F A028257 For a number x (here sqrt(3)), define a(1)<=a(2)<=a(3)<=.. so that x 
               = 1/a(1) + 1/a(1)a(2) + 1/a(1)a(2)a(3) + .. by x(1)=x, a(n) = ceil(1/
               x(n)), x(n+1) = x(n)a(n)-1.
%t A028257 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]]; EngelExp[N[3^(1/2),7! ],50] [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Jun 08 2009]
%Y A028257 Cf. A006784 (for definition of Engel expansion).
%Y A028257 Sequence in context: A049875 A087989 A103356 this_sequence A100228 A111003 
               A140182
%Y A028257 Adjacent sequences: A028254 A028255 A028256 this_sequence A028258 A028259 
               A028260
%K A028257 nonn
%O A028257 1,2
%A A028257 Naoki Sato (naoki(AT)math.toronto.edu)
%E A028257 Better name and more terms from Simon Plouffe (simon.plouffe(AT)gmail.com).