This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
nn = 250; t = Select[Union[Flatten[Table[a*b + b*c + a*c + 1, {a, nn}, {b, a, nn}, {c, b, nn}]]], # <= 2*nn + 1 &]; Complement[Range[2*nn + 1], t]
A 1 X 1 X 1 block has surface area 6. A 1 X 1 X 2 block has surface area 10. No n1 X n2 X n3 block of intermediate size exists, so there is no way to create an n1 X n2 X n3 block with surface area 8.
from sympy import integer_nthroot
def aupto(lim):
e, r, lim2 = set(range(2, lim+1, 2)), set(), integer_nthroot(lim//2, 2)[0]
for n1 in range(1, lim2):
for n2 in range(n1, lim2):
for n3 in range(n2, lim+1):
r.add(2*(n1*n2 + n1*n3 + n2*n3))
return sorted(e - r)
print(aupto(1000)) # Michael S. Branicky, Feb 04 2021
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