|
%I #11 Mar 16 2021 05:11:22
%S 2,10,24,45,71,104,143,188,239,296,359,427,502,583,670,763,862,967,
%T 1078,1195,1318,1447,1582,1723,1870,2023,2181,2346,2517,2694,2877,
%U 3066,3261,3462,3669,3882,4101,4326,4557,4794,5037,5286,5541,5802,6069,6342,6621
%N Number of iterations of the sine function to be less than 1/n with an initial argument of Pi/2 radians.
%F Lim_{n->infinity} a(n)/n^2 = 3. - _Jon E. Schoenfield_, Mar 16 2021
%e Let t_(j+1) = sin(t_j) for j >= 0 with t_0 = Pi/2. Then t_9 = 0.50217... > 1/2, whereas t_10 = sin(t_9) = sin(0.50217...) = 0.48132... < 1/2, so a(2)=10.
%t A092906[n_] := Block[{k = 1}, While[ N[ Nest[ Sin, Pi/2, k], 64] >= 1/n, k++ ]; k]; Table[ A092906[n], {n, 47}]
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Mar 13 2004
|
