Values of n for which Integer Solutions to n = x^3 + y^3 + 2 z^3 are Unknown

Open Question

For the following values of $n$, it is not known whether the indeterminate equation:

$n = x^3 + y^3 + 2 z^3$

has any integer solutions:

$76, 148, 183, 230, 356, 418, 428, 445, 482, 491, 580, 671, 788, 931, 967$

Historical Note

1997: David Wells: Curious and Interesting Numbers (2nd ed.) reports that the given list of positive integers are the only ones known under $1000$.

The author of this webpage has been unable to determine whether this statement is still accurate.

Sources

• 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $76$