A092906 Number of iterations of the sine function to be less than 1/n with an initial argument of Pi/2 radians.

2, 10, 24, 45, 71, 104, 143, 188, 239, 296, 359, 427, 502, 583, 670, 763, 862, 967, 1078, 1195, 1318, 1447, 1582, 1723, 1870, 2023, 2181, 2346, 2517, 2694, 2877, 3066, 3261, 3462, 3669, 3882, 4101, 4326, 4557, 4794, 5037, 5286, 5541, 5802, 6069, 6342, 6621

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Formula

Lim_{n->infinity} a(n)/n^2 = 3. - Jon E. Schoenfield, Mar 16 2021

Example

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.

Mathematica

A092906[n_] := Block[{k = 1}, While[ N[ Nest[ Sin, Pi/2, k], 64] >= 1/n, k++ ]; k]; Table[ A092906[n], {n, 47}]

Crossrefs

Sequence in context: A293412 A224837 A049450 * A244383 A295053 A130016

Adjacent sequences: A092903 A092904 A092905 * A092907 A092908 A092909

Keyword

nonn

Author

Robert G. Wilson v, Mar 13 2004

Status

approved