There are infinitely many polynomials of order 4 that will give these as the first four numbers and any one of these could be "the" rule. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
The simplest polynomial, of order 3, is
U(n) = (-13n^3 + 90n^2 - 227n + 384)/6 for n = 1, 2, 3, ...
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29 and 31 are prime. The rest are composite numbers.
1.1481
Maximum = 45 Minimum = 14 Range = Max - min = 45 - 14 = 31
There are not many numbers in the sequence here, but one solution that holds for this series is to take the first number, double it to get the second number, add 1 to get the next number, and repeat. So, the pattern would continue as follows: 1, 2, 3, 6, 7, 14, 15, 30, 31, 62, 63
31 x 14 = 434