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

main.m
function result = smallest_odd_composite()
    n = 3; % start with the first odd composite number 
    primes = primes(n); % generate all primes less than or equal to n
    while true
        if isprime(n) % if n itself is prime, move to the next number
            n = n + 2;
            primes = primes(primes < n); % update the list of primes
            continue;
        end
        can_be_written = false; % assume that n cannot be written in the form p + 2k^2
        for p = primes
            k = sqrt((n - p) / 2);
            if k == floor(k) % check if (n - p)/2 is a perfect square
                can_be_written = true; % if so, n can be written in the form p + 2k^2
                break;
            end
        end
        if ~can_be_written % if n cannot be written in the form p + 2k^2, we have our answer
            result = n;
            return;
        end
        n = n + 2; % move to the next odd composite number
    end
end
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