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.

9 = 7 + 2×1² 15 = 7 + 2×2² 21 = 3 + 2×3² 25 = 7 + 2×3² 27 = 19 + 2×2² 33 = 31 + 2×1²

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?

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