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Greedy Egyptian fraction expansion for 4/Pi
0

%I #2 Mar 30 2012 17:23:26

%S 1,4,44,1953,4179942,42836179578838,3958573977160882295479936105,

%T 36328295343356352083453782833218820307659379901717630389

%N Greedy Egyptian fraction expansion for 4/Pi

%C Sum_{n>=0}1/a(n)=4/Pi

%C Truncating the series to three terms yields the convergent 22/7 as an approximation to Pi:

%C 1+1/4+1/44=14/11=4/(22/7)

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions">Greedy algorithm for Egyptian fractions</a>

%o (PARI) x=4/Pi; for (k=0,7,d=ceil(1/x);x=x-1/d;print(d,", "))

%Y Cf. A088538, A154956, A156618.

%K frac,nonn

%O 0,2

%A _Jaume Oliver Lafont_, Feb 24 2009