The numbers are 352, 354, 356, 358 and 360.
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Any pair of consecutive numbers will have an odd total. 10 and 12 are consecutive even numbers that total 22.
The numbers are 38, 40 and 42.
There is no set of four consecutive numbers (odd or even) whose sum equals 169.
There are no two consecutive even numbers whose sum is 100. It is easily proved.
The numbers are 82, 84, 86 and 88.