As to the convergenge to zero: note that the convergents of the [continuous fraction for $\pi$][1] provide a rational approximation $|\pi - p_n/q_n| < 1/q_nq_{n+1}$ so that $\sin p_n\to 0$.

The sequence of numerators $0, 1, 3, 22, 333, 355,\dots$ is OEIS' [A002485][2]. [1]:http://oeis.org/A001203 [2]:http://oeis.org/A002485

As to the convergenge to zero: note that the convergents of the continuous fraction for $\pi$ provide a rational approximation $|\pi - p_n/q_n| < 1/q_nq_{n+1}$ so that $\sin p_n\to 0$.

The sequence of numerators $0, 1, 3, 22, 333, 355,\dots$ is OEIS' A002485.

As to the convergenge to zero: note that the convergents of the continuous fraction for $\pi$ provide a rational approximation $|\pi - p_n/q_n| < 1/q_nq_{n+1}$ so that $\sin p_n\to 0$.

As to the convergenge to zero: note that the convergents of the [continuous fraction for $\pi$][1] provide a rational approximation $|\pi - p_n/q_n| < 1/q_nq_{n+1}$ so that $\sin p_n\to 0$.

The sequence of numerators $0, 1, 3, 22, 333, 355,\dots$ is OEIS' [A002485][2]. [1]:http://oeis.org/A001203 [2]:http://oeis.org/A002485