Using $4.479 times 10^{8}$ $psi(3686)$ events collected with the BESIII detector, we search for the decays $psi(3686) rightarrow e^{+}e^{-}chi_{c0,1,2}$ and $chi_{c0,1,2} rightarrow e^{+}e^{-}J/psi$. The decays $psi(3686) rightarrow e^{+}e^{-}chi_{c0,1,2}$ and $chi_{c0,1,2} rightarrow e^{+}e^{-}J/psi$ are observed for the first time. The measured branching fractions are $mathcal{B}(psi(3686) rightarrow e^{+}e^{-}chi_{c0,1,2}) = (11.7 pm 2.5 pm 1.0)times10^{-4}$, $(8.6 pm 0.3 pm 0.6)times10^{-4}$, $(6.9 pm 0.5 pm 0.6)times10^{-4}$, and $mathcal{B}(chi_{c0,1,2} rightarrow e^{+}e^{-}J/psi) = (1.51 pm 0.30 pm 0.13)times10^{-4}$, $(3.73 pm 0.09 pm 0.25)times10^{-3}$, $(2.48 pm 0.08 pm 0.16)times10^{-3}$. The ratios of the branching fractions $frac{mathcal{B}(psi(3686) rightarrow e^{+}e^{-}chi_{c0,1,2})}{mathcal{B}(psi(3686) rightarrow gammachi_{c0,1,2})}$ and $frac{mathcal{B}(chi_{c0,1,2} rightarrow e^{+}e^{-}J/psi)}{mathcal{B}(chi_{c0,1,2} rightarrow gamma J/psi)}$ are also reported.
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