The numbers are 39, 40 and 41.
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Their sum is 15.
The numbers are 38, 40 and 42.
The average must be 360/3 ie 120 so the integers are 118, 120 and 122.
There are no three consecutive odd integers who's sum equals 13.
The three consecutive even numbers with a sum of 138 are 44, 46 and 48.