Question about semi-twin primes

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Has anyone ever studied the following numbers? I came up with the name semi-twin primes as I could not find any reference on this topic. These are prime numbers $p$ such that $p+1 = 2q$, with $q$ being a prime. The list starts with $p= 3, 5, 13, 37, 61, 73$ and so on. I searched Google for $3, 5, 13, 37, 61, 73$ but didn't find anything.