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%I #4 Mar 30 2012 17:31:15
%S 1,4,4,6,8,9,11,13,14,16,17,19,21,23,25,26,27,30,31,33,34,36,38,40,41,
%T 43,45,46,47,49,53,53,54,56,58,60,61,62,65,66,67,70,71,72,75,76,78,80,
%U 83,83,84,87,89,89,91,93,94,96,98,99,100,103,105,107,107,109,112,112
%N Number of bisections to an inscribed triangle to approximate Pi (A000796) to n decimal digits of accuracy.
%D Howard Anton, Irl C. Bivens and Stephen L. Davis, Calculus, Early Transcendentals, 7th Edition, John Wiley & Sons, Inc., NY, Section 6.1 An Overview of the Area Problem, page 372-377.
%D William Dunham, The Calculus Gallery, Masterpieces from Newton to Lebesgue, Princeton University Press, Princeton, NJ 2005, page 56-57.
%F a(n) = 3*2^n*sqrt(2- sqrt(2+ sqrt(2+ ... sqrt(2+ sqrt(3))...))).
%F A(n) in Table 6.1.1 = Sin( 2Pi/n )*n/2. - Anton.
%t $MaxExtraPrecision =128; p=RealDigits[ Pi, 10, 100][[1]]; f[n_] := 3*2^(n)*Sqrt[2 - Nest[ Sqrt[2 + # ] &, Sqrt[3], n - 1]]; g[n_] := Block[{k = 1, q = Take[p, n + 1]}, While[ Take[ RealDigits[ f[k], 10, 100][[1]], n + 1] != q, k++ ]; k]; Table[ g[n], {n, 69}]
%Y Cf. A000796.
%K nonn,base
%O 1,2
%A _Robert G. Wilson v_, Apr 20 2005
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