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

Author

Treanungkur Mal, Jul 02 2021

Keywords

• nonn
• more

Examples

			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...
		

Crossrefs

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

Programs

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

Extensions

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