 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

Choose the <sequence>
$$
\boxed{a_n=(-1)^n\qquad(n\geq1).}
$$
Every even index is a <peak of a sequence> $(a_n)$, since its value is $1$ and all later values are at most $1$. Every odd index is a <peak of a sequence> $(-a_n)$ for the same reason. Both <sets> of indices are infinite.

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