It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.

$$\begin{array}{r}9=7+2\times 1^2\\ 15=7+2\times 2^2\\ 21=3+2\times 3^2\\ 25=7+2\times 3^2\\ 27=19+2\times 2^2\\ 33=31+2\times 1^2\end{array}$$

It turns out that the conjecture was false.

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?