The sequence $1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201, \dots$
is defined by $T_1 = T_2 = T_3 = 1$ and $T_n = T_{n - 1} + T_{n - 2} + T_{n - 3}$.
It can be shown that $27$ does not divide any terms of this sequence.
In fact, $27$ is the first odd number with this property.
Find the $124$th odd number that does not divide any terms of the above sequence.
Solution
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