Goldbach's Other Conjecture
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{align} 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{align}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?