  The problem of sequentially finding an independent and identically
distributed (i.i.d.) sequence that is drawn from a probability distribution
$F_1$ by searching over multiple sequences, some of which are drawn from $F_1$
and the others of which are drawn from a different distribution $F_0$, is
considered. The sensor is allowed to take one observation at a time. It has
been shown in a recent work that if each observation comes from one sequence,
Cumulative Sum (CUSUM) test is optimal. In this paper, we propose a new
approach in which each observation can be a linear combination of samples from
multiple sequences. The test has two stages. In the first stage, namely
scanning stage, one takes a linear combination of a pair of sequences with the
hope of scanning through sequences that are unlikely to be generated from $F_1$
and quickly identifying a pair of sequences such that at least one of them is
highly likely to be generated by $F_1$. In the second stage, namely refinement
stage, one examines the pair identified from the first stage more closely and
picks one sequence to be the final sequence. The problem under this setup
belongs to a class of multiple stopping time problems. In particular, it is an
ordered two concatenated Markov stopping time problem. We obtain the optimal
solution using the tools from the multiple stopping time theory. Numerical
simulation results show that this search strategy can significantly reduce the
searching time, especially when $F_{1}$ is rare.
