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

The sum of three consecutive odd integers is 147

2k - 1 + 2k + 1 + 2k + 3 = 147

by solving we find

k = 24

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2*24 - 1 = 47

2*24 + 1 = 49

2*24 + 3 = 51

the three integers are 47, 49 and 51.