  One can use the number theoretic idea of the notion of natural density
\cite{B1} to define topological s-torsion elements (which form the
statistically characterized subgroups, recently developed in \cite{DPK})
extending Armacost's idea of topological torsion elements. We follow in the
line of Armacost who had posed the famous classical problem for "description of
topological torsion elements" of the circle group. In this note we consider the
natural density version of Armacost's problem and present a complete
description of topological s-torsion elements in terms of the support, for all
arithmetic sequences which also provides the solution of Problem 6.10 posed in
\cite{DPK} .
