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Leaving aside 2, you will get so-called singly even numbers, those which are divisible by 2 but not by 4. (e.g. 2 + 4 = 6)

The sum of consecutive even integers (n) + (n+2) is 2n +2, which is double the intervening odd number (n+1).

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Q: What numbers do you get when you add consecutive even numbers?
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