A345670 a(n) is the smallest integer k > 0 such that 10^(-n-1) < |cos(k) - round(cos(k))| < 10^(-n).

1, 3, 11, 44, 22, 16685, 5325, 1775, 710, 355, 104348, 312689, 1146408, 20530996, 10838702, 5419351, 165707065, 411557987

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Example

For n = 4, a(n) = 22 because 22 is the smallest positive integer k such that 10^(-5) < |cos(k) - round(cos(k))| < 10^(-4): |cos(22) - round(cos(22))| = 0.0000391...

Prog

(C++)
/* Only suitable for computing a(0) to a(15) due to double precision limits. */
#include <iostream>
#include <cmath>
using namespace std;
int main(int argc, char** argv) {
    for (int n=0; n<=15; n++) {
        for (int k=1; k<=20530996; k++) {
            double x = cos(k);
            double val = abs(x-round(x));
            if (val < pow(10, -n) && val > pow(10, -n-1)){
                cout << k <<", ";
                break;
            }
        }
    }
}
(PARI) a(n) = my(k=1, ok=0, x); while (!ok, x=abs(cos(k) - round(cos(k))); ok = (x>1/10^(n+1)) && (x < 1/10^n); if (ok, break); k++); k; \\ Michel Marcus, Jul 02 2021

Crossrefs

Cf. A346033 (sin), A345404 (tan).

Sequence in context: A153476 A107290 A302333 * A370998 A239392 A122393

Adjacent sequences: A345667 A345668 A345669 * A345671 A345672 A345673

Keyword

nonn,more

Author

Treanungkur Mal, Jul 02 2021

Extensions

a(16)-a(17) from Jon E. Schoenfield and Sean A. Irvine, Jul 03 2021

Status

approved