%I A028254
%S A028254 1,3,5,5,16,18,78,102,120,144,251,363,1402,31169,88630,184655,259252,
%T A028254 298770,4196070,38538874,616984563,1975413035,5345718057,27843871197,
%U A028254 54516286513,334398528974,445879679626
%N A028254 Engel expansion of sqrt(2).
%C A028254 For a number x (here sqrt(2)), 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.
%H A028254 T. D. Noe, <a href="b028254.txt">Table of n, a(n) for n=1..300</a>
%H A028254 Naoki Sato, <a href="http://www.math.toronto.edu/~naoki/">Home page</
               a>
%H A028254 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EngelExpansion.html">Engel Expansion</a>
%H A028254 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PythagorassConstant.html">Pythagoras's Constant</a>
%t A028254 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[2^(1/2),7! ],47] [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Jun 08 2009]
%Y A028254 Cf. A006784 (for definition of Engel expansion).
%Y A028254 Sequence in context: A089167 A028265 A084041 this_sequence A137780 A079372 
               A055382
%Y A028254 Adjacent sequences: A028251 A028252 A028253 this_sequence A028255 A028256 
               A028257
%K A028254 nonn
%O A028254 1,2
%A A028254 Naoki Sato (naoki(AT)math.toronto.edu)
%E A028254 More terms from Simon Plouffe (simon.plouffe(AT)gmail.com), Jan 05, 2002