Problem 225

Tribonacci non-divisors

The sequence 1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201 ...

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.

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