A337371 Integers k with abs(sin(k)) < 1/k.

1, 3, 22, 44, 355, 710, 1065, 1420, 1775, 2130, 2485, 2840, 3195, 312689, 1146408, 5419351, 10838702, 6167950454, 21053343141, 42106686282, 63160029423, 84213372564, 105266715705, 8958937768937, 17917875537874, 428224593349304, 856449186698608, 6134899525417045

Offset: 1

Author

Anian Brosig, Aug 25 2020

Keywords

• nonn

Comments

The values > 1 appear to be a subset of the numerators of continued fractions of Pi (A002485) (and/or Pi/2: A096456) and their multiples. Is it possible to find a term k here but not in |A332095| (k |tan k| < 1)? - M. F. Hasler, Oct 09 2020

Crossrefs

Cf. A092328, A332095, A046965, A088306, A337249, A332095.

Programs

Mathematica

Select[Range[3200], Abs[Sin[#]] < 1/# &] (* Amiram Eldar, Aug 25 2020 *)

PARI

print1(1);apply( n-> forstep(n=n,oo,n,abs(sin(n))<1/n||return; print1(","n)), contfracpnqn(c=contfrac(Pi),#c)[1,]); \\ M. F. Hasler, Oct 09 2020

Python

import numpy as np
for x in range(1, 10**9):
    if np.abs(np.sin(x)) < 1/x:
        print(x, end=", ")

Extensions

More terms from M. F. Hasler, Oct 09 2020