The sum of any two consecutive integers is odd. Try it out.
3 + 4 = 7
4 + 5 = 9
If it works for those, it works for all of them.
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The two consecutive, even integers are 350 and 352.
No two consecutive even integers satisfy that request.
The sum of the first four non-negative, consecutive, even integers is 20.
3 consecutive even integers whose sum is 396 are 130, 132 and 134.
The smallest of seven consecutive even integers whose sum is 700 is 94.