%I A014013
%S A014013 7,790,749896,1270073831726,3264508855407706377676178,
%T A014013 18710490702451568752627532846550947209438603938993,
%U A014013 973885998866223812020176506328879365154595266536880449064639606785601754387311047869879785998363014
%N A014013 Alternating Egyptian fraction expansion of Pi.
%H A014013 <a href="Sindx_Ed.html#Egypt">Index entries for sequences related to 
               Egyptian fractions</a>
%F A014013 pi-3 = sum(k>=1, (-1)^(k+1)/a(k)) = 0.14159...; a(n)=(-1)^(n+1)*u(n) 
               where u(1)=7, u(n)=trunc(1/(Pi-3-sum(k=1, n-1, 1/u(k)))) and trunc(x)=floor(x) 
               if x>=0, trunc(x)=ceil(x) if x<0
%e A014013 1/(Pi-3-1/7+1/790) = 749896.4427... hence a(3)=749896
%Y A014013 Sequence in context: A114911 A162089 A020470 this_sequence A001467 A047788 
               A087350
%Y A014013 Adjacent sequences: A014010 A014011 A014012 this_sequence A014014 A014015 
               A014016
%K A014013 nonn
%O A014013 1,1
%A A014013 Simon Plouffe (simon.plouffe(AT)gmail.com)