33
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6+7+8+9=30
3332, 3333 and 3334 add up to 9999 - there are no three consecutive numbers that add up to 10,000.
30 + 32 + 34 = 96
The numbers are 26, 28, 30, 32, 34 and also 28, 29, 30, 31, 32.
There is no such set of numbers.