A161559 - OEIS

%I #5 Mar 31 2012 12:38:24

%S 2,11,54,136,1473,3483,36244,41086,305728,379955,582669,4540387,

%T 5020443,22096761,24228660,48364856,178868536,234516235,524137295,

%U 1096104266,11627672572,19828856452,31372689367,47247829739,701124643395

%N Engel expansion of tan(1/2).

%H <a href="/index/El#Engel">Index to sequences related to Engel expansions</a>

%e A161011 = 0.546302.... = 1/2+1/(2*11)+1/(2*11*54)+1/(2*11*54*136)+ ...

%t 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[Tan[1/2],6! ],50]

%Y Cf. A006784.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jun 13 2009

%E Example added by _R. J. Mathar_, Oct 04 2009