OFFSET
1,2
COMMENTS
A024810(n) is the number of x in the interval (1/2^(n+1), 1) such that f(x) = sin(1/x) = 0, for n >= 1. It is well known that the function f(x) oscillates indefinitely around 0 as x approaches zero.
Equivalently, the number of roots of the sine function on [1, 2^(n+1)], given by floor(2*2^n/Pi). - M. F. Hasler, Oct 25 2019
EXAMPLE
From M. F. Hasler, Oct 25 2019: (Start)
The first nonzero root of the sine function is at Pi ~ 3.14, so there is one on [1, 4] = [1, 2^(1+1)], whence a(1) = A024810(1) = 1.
On [1, 8] = [1, 2^(2+1)], there is one more root, x = 2*Pi ~ 6.28. Therefore A024810(2) = 2 (number of roots) and a(2) = a(1) + 2 = 3.
PROG
(PARI) my(s=0); for(n=0, 29, s+=floor(4*2^n/Pi); print1(s, ", ")) \\ Hugo Pfoertner, Oct 24 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 30 2010
EXTENSIONS
Edited by M. F. Hasler, following a remark by Kevin Ryde, Oct 24 2019
Data corrected and extended by M. F. Hasler, Oct 25 2019
STATUS
approved