Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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