OFFSET
1,1
COMMENTS
If b is the sum of two positive cubes in exactly n ways, then b*c^3 is the sum of two positive cubes in at least n ways for all c > 0. So A011541(i)*c^3 is a candidate for unknown Taxi-cab numbers. a(6) = 79 is an interesting example that is related to this case. Additionally, the benefit of this simple fact is the determination of upper bounds for unknown Taxi-cab numbers in relatively easy way.
The inequalities that are given in the comment section of A011541 are:
So a(6) <= 101, a(7) <= 127, a(8) <= 139.
EXAMPLE
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Altug Alkan, May 26 2016
STATUS
approved