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A346033 a(n) is the smallest integer k > 0 such that 10^(-n-1) < |sin(k) - round(sin(k))| < 10^(-n).

%I A346033 #60 Jul 03 2021 05:41:43
%S A346033 1,2,14,55,33,11,35489,46849,50754,51819,52174,260515,1719612,573204,
%T A346033 21104200,37362253,42781604,122925461,534483448
%N A346033 a(n) is the smallest integer k > 0 such that 10^(-n-1) < |sin(k) - round(sin(k))| < 10^(-n).
%e A346033 For n = 3, a(n) = 55 because 55 is the smallest positive integer k such that 10^(-4) < |sin(k) - round(sin(k))| < 10^(-3): |sin(55) - round(sin(55))| = 0.000244....
%o A346033 (C++)
%o A346033 /* Only suitable for computing a(0) to a(15) due to double precision limits. */
%o A346033 #include <iostream>
%o A346033 #include <cmath>
%o A346033 using namespace std;
%o A346033 int main(int argc, char** argv) {
%o A346033     for (int n=0; n<=15; n++) {
%o A346033         for (int k=1; k<=37362253; k++){
%o A346033             double x = sin(k);
%o A346033             double val = abs(x-round(x));
%o A346033             if (val < pow(10, -n) && val > pow(10, -n-1)) {
%o A346033                 cout << k <<", ";
%o A346033                 break;
%o A346033             }
%o A346033         }
%o A346033     }
%o A346033 }
%Y A346033 Cf. A096456, A345404.
%K A346033 nonn,more
%O A346033 0,2
%A A346033 _Treanungkur Mal_, Jul 01 2021
%E A346033 a(16)-a(18) from _Jon E. Schoenfield_ and _Sean A. Irvine_, Jul 02 2021