How can one fill the gaps in?
How can one fill the gaps in 30,53,73,73,__,201,__? Any way you want. We have 5 known numbers, and its pretty easy to show that we can make the other 2 numbers be any integers, or any fractions, or any irrational number, or any complex number, or in fact any non-transcendental number we want, by using a 7th order equation with the proper coefficients, so f(0) = 30, f(1) = 53, f(2) = 73, and so on, Pick the coefficients correctly and f(4) can be zero. Pick different coefficients and f(4) can be the square root of 2. You want f(4) to be the square root of 17 and f(6) to be the square root of -1? Youre going to have 7 really ugly coefficients and f(7) is going to be *really* weird, but you can do it. Now, if you want the *simplest* pattern that makes things work, thats a different question - and quite possibly theres multiple competing ways to do it that have a valid claim to be simplest when applying different definitions of simple.