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Denominators of Egyptian fraction for Pi-3 whose partial sums are the convergents
3

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

%S 7,-742,11978,-3740526,1099482930,-2202719155,6600663644,-26413901692,

%T 96840976853,-496325469560,2346251883960,-44006595799206,

%U 1345586183756654,-4127747481719463,10251870941174304

%N Denominators of Egyptian fraction for Pi-3 whose partial sums are the convergents

%C Numerators are all 1.

%e 3+1/a(0)=22/7

%e 3+1/a(0)+1/a(1)=333/106

%e 3+1/a(0)+1/a(1)+1/a(2)=355/113

%o (PARI) c0=3; for (k=2,30,m=contfracpnqn(contfrac(Pi,k));c1=m[1,1]/m[2,1];print1(1/(c1-c0),", ");c0=c1;)

%Y Cf. A001466, A014013, A156019, A156020, A002485, A002486.

%K sign

%O 0,1

%A _Jaume Oliver Lafont_, Feb 11 2009