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For each $m \\geq 3$, write $p_{m-1} + 1 = L_m R_m$ with $L_m$ the largest prime factor. Restricting to those $m$ for which $L_m > m$ (equivalently, $m \\in \\text{A223881}$), we obtain a multiset of values $R_m$. Since $p_{m-1}+1$ is even and $L_m > 3$ is odd, all values of $R_m$ are strictly even. Sorting the distinct $R_m$ by decreasing frequency yields a new sequence beginning $2, 6, 4, 8, 10, 12, 14, 16 \\dots$. 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For each $m \\geq 3$, write $p_{m-1} + 1 = L_m R_m$ with $L_m$ the largest prime factor. Restricting to those $m$ for which $L_m > m$ (equivalently, $m \\in \\text{A223881}$), we obtain a multiset of values $R_m$. Since $p_{m-1}+1$ is even and $L_m > 3$ is odd, all values of $R_m$ are strictly even. Sorting the distinct $R_m$ by decreasing frequency yields a new sequence beginning $2, 6, 4, 8, 10, 12, 14, 16 \\dots$. 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