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%I #14 Aug 23 2021 06:10:24
%S 7,-790,12016,-3748629,1730431227,-3015428685,8172837003,-34313104062,
%T 114738541304,-620832653094,2474837590227,-45157370341559,
%U 1726856191927439,-6094457427533473,12791098836150787,-51642743340781227,325724575136738920,-1813676066719263909
%N Reciprocals of the deviation of continued fraction convergents from Pi.
%C Clearly the terms alternate in sign, but the initial choice of sign was arbitrary.
%e The first convergent to Pi, 3, is just over 1/7 too low, so 7 is the first term.
%e The second convergent, 22/7, is 0.001264+ too high, which is just over 1/790, so -790 is the second term.
%o (PARI) for(x=1,10,t=contfracpnqn(contfrac(Pi,x));print(truncate(1/(Pi-t[1,1]/t[2,1]))))
%Y Cf. A001203.
%K sign
%O 1,1
%A _Phil Carmody_, Dec 06 2009
%E More terms from _Jinyuan Wang_, Aug 23 2021
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