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We consider the symmetric multiple zeta values in $\mathcal{S}_m$ withoutmodulo $\pi^2$ reduction for indices in which $1$ and $3$ appear alternately.We investigate those values that can be expressed as a polynomial of theRiemann zeta values, and give a conjecturally complete list of explicitformulas for such values.

$t$-adic symmetric multiple zeta values for indices in which $1$ and $3$ appear alternately