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Problem of the Week
Problem D
Three Sequences

Three sequences each have first term \(3\). In the first sequence, each term after the first term is \(15\) more than the previous term. In the second sequence, each term after the first term is \(16\) more than the previous term. In the third sequence, each term after the first term is \(18\) more than the previous term. The three sequences continue indefinitely.

The first sequence has terms 3, 18, 33, 48, 63, 78, 93, and so on. The second sequence has terms 3, 19, 35, 51, 67, 83, 99, 115, 131, 147, and so on. The third sequence has terms 3, 21, 39, 57, 75, 93, 111, 129, 147, and so on.

Determine all numbers between \(3\) and \(2025\), inclusive, that are common to all three sequences.