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A014013 Alternating Egyptian fraction expansion of Pi-3. 4

%I

%S 7,790,749896,1270073831726,3264508855407706377676178,

%T 18710490702451568752627532846550947209438603938993

%N Alternating Egyptian fraction expansion of Pi-3.

%C The next term has 99 digits.

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%F 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) = ceiling(x) if x < 0.

%e 1/(Pi - 3 - 1/7 + 1/790) = 749896.4427... hence a(3)=749896.

%K nonn

%O 1,1

%A _Simon Plouffe_

%E Title correction by _Stanislav Sykora_, May 05 2012

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)