-701, -703, -705, -707, -709 and -711.
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There is no set of three consecutive odd or even integers whose sum is negative 31.
96
The six consecutive integers greater than -7 are: -7, -6, -5, -4, -3, -2
-9 -6 -3 0 3 6 9
There is no set of three consecutive even integers whose sum is 999. There are two other sets; one is odd, the other is mixed. The odd set is 331, 333 and 335. The mixed set is 332, 333 and 334.