Sum-product numbers: A potentially ill-defined sequence

[Alonso Del Arte]

Puzio's proof on PlanetMath that the number of sum-product numbers in
any base is finite
<http://planetmath.org/?op=getobj&from=objects&id=7743> to me suggests
a sequence: Maximum number of digits a sum-product number can
theoretically have in base n. Then a(10) = 84. But Morris's proof
specific for binary
<http://planetmath.org/?op=getobj&from=objects&id=7739> suggests
theoretically that a(2) = 1 in much the same way that Wilson's proof
for base 10 at A038369 would suggest that a(10) of this sequence = 3.

Alonso