

A172265


Partial sums of A024810(n) = floor(2^(n+1)/Pi).


1



1, 3, 8, 18, 38, 78, 159, 321, 646, 1297, 2600, 5207, 10422, 20852, 41712, 83433, 166876, 333762, 667534, 1335078, 2670166, 5340342, 10680695, 21361402, 42722816, 85445645, 170891304, 341782622, 683565259, 1367130534, 2734261085, 5468522187, 10937044391
(list;
graph;
refs;
listen;
history;
text;
internal format)



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


LINKS

Table of n, a(n) for n=1..33.


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.
On [1, 16] = [1, 2^(3+1)], there are a total of five roots, x = k*Pi with k = 1,...,5. Therefore A024810(3) = 5 and a(3) = a(2) + 5 = 8. The formula floor(2^(n+1)/Pi) for A024810(n), by definition equal to the increment a(n)  a(n1), becomes obvious. (End)


PROG

(PARI) my(s=0); for(n=0, 29, s+=floor(4*2^n/Pi); print1(s, ", ")) \\ Hugo Pfoertner, Oct 24 2019


CROSSREFS

Cf. A024810.
Sequence in context: A104187 A051633 A131051 * A258272 A117727 A117713
Adjacent sequences: A172262 A172263 A172264 * A172266 A172267 A172268


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



