Problem 225

Tribonacci non-divisors

The sequence 1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201 …
is defined by T₁ = T₂ = T₃ = 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.

三阶斐波那契数的非约数

序列1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201 …
的定义为T₁ = T₂ = T₃ = 1以及T_n = T_n-1 + T_n-2 + T_n-3。

可以说明，27不能整除这个序列中的任何一项。事实上，27是第一个拥有这一性质的奇数。

求第124个不能整除上述序列中任何一项的奇数。