A345670 - OEIS

%I #61 Jul 10 2021 23:28:55

%S 1,3,11,44,22,16685,5325,1775,710,355,104348,312689,1146408,20530996,

%T 10838702,5419351,165707065,411557987

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

%e 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...

%o (C++)

%o /* Only suitable for computing a(0) to a(15) due to double precision limits. */

%o #include <iostream>

%o #include <cmath>

%o using namespace std;

%o int main(int argc, char** argv) {

%o     for (int n=0; n<=15; n++) {

%o         for (int k=1; k<=20530996; k++) {

%o             double x = cos(k);

%o             double val = abs(x-round(x));

%o             if (val < pow(10, -n) && val > pow(10, -n-1)){

%o                 cout << k <<", ";

%o                 break;

%o             }

%o         }

%o     }

%o }

%o (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

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

%K nonn,more

%O 0,2

%A _Treanungkur Mal_, Jul 02 2021

%E a(16)-a(17) from _Jon E. Schoenfield_ and _Sean A. Irvine_, Jul 03 2021