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%I #10 Oct 20 2014 17:15:18
%S 2,4,4,15,17,77,101,119,143,250,362,1401,31168,88629,184654,259251,
%T 298769,4196069,38538873,616984562,1975413034,5345718056,27843871196,
%U 54516286512,334398528973,445879679625,495957494385,2450869042060,2629541150528,4088114099884
%N Kochanski approximates to sqrt(2) starting with R_0=3, S_0=2.
%H Henryk Fuks, <a href="http://arxiv.org/abs/1111.1739">Adam Adamandy Kochanski's approximations of pi: reconstruction of the algorithm</a>, arXiv preprint arXiv:1111.1739, 2011. Math. Intelligencer, Vol. 34 (No. 4), 2012, pp. 40-45.
%F Definitions 1 and 2 of Fuks (2011) give formulas.
%o (PARI)
%o galpha(alpha, R, S) = {floor((alpha - floor(alpha))/(R - alpha*S));}
%o fuks() = { n = 29; default(realprecision, 200); alpha = sqrt(2); R = 3; S = 2; x = galpha(alpha, R, S); print1(x, ", "); for (i=1, n, R = R*(x+1) + floor(alpha); S = S*(x+1) + 1; x = galpha(alpha, R, S); print1(x, ", "););}
%o \\ _Michel Marcus_, Feb 07 2013
%Y Cf. A191642.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Jan 23 2013
%E More terms from _Michel Marcus_, Feb 07 2013
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