Every odd number can be written in a form 2k +1, where k is integer.

Thus the three consecutive odd integers can be written as:

2k - 1, 2k + 1 and 2k + 3, where k is integer.

Three times the middle is 15 more than the sum of the two:

3(2k + 1) = 15 + 2k - 1 + 2k + 3

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click here to see the equation solved for k

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k = 7

2k - 1 = 2*(7) - 1 = 13

2k + 1 = 2*(7) + 1 = 15

2k + 3 = 2*(7) + 3 = 17

The three consecutive odd integers are 13, 15 and 17.