Even Integers not Sum of 2 Twin Primes

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The following even integers cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes:

$2, 4, 94, 96, 98, 400, 402, 404, \ldots$

This sequence is A007534 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).