Smallest positive integer written as the sum of two integer cubes in n ways
In
number theory, the n-th cabtaxi number, typically denoted Cabtaxi(n), is defined as the smallest positive
integer that can be written as the sum of two positive or negative or 0cubes in n ways. Such numbers exist for all n, which follows from the analogous result for
taxicab numbers.
Known cabtaxi numbers
Only 10 cabtaxi numbers are known (sequence A047696 in the
OEIS):
History
Cabtaxi(5), Cabtaxi(6) and Cabtaxi(7) were found by
Randall L. Rathbun; Cabtaxi(8) was found by
Daniel J. Bernstein. Cabtaxi(9) was found by Duncan Moore, using Bernstein's method. Cabtaxi(10) was first reported as an upper bound by
Christian Boyer in 2006 and verified as Cabtaxi(10) by
Uwe Hollerbach and reported on the
NMBRTHRY mailing list on May 16, 2008.
Smallest positive integer written as the sum of two integer cubes in n ways
In
number theory, the n-th cabtaxi number, typically denoted Cabtaxi(n), is defined as the smallest positive
integer that can be written as the sum of two positive or negative or 0cubes in n ways. Such numbers exist for all n, which follows from the analogous result for
taxicab numbers.
Known cabtaxi numbers
Only 10 cabtaxi numbers are known (sequence A047696 in the
OEIS):
History
Cabtaxi(5), Cabtaxi(6) and Cabtaxi(7) were found by
Randall L. Rathbun; Cabtaxi(8) was found by
Daniel J. Bernstein. Cabtaxi(9) was found by Duncan Moore, using Bernstein's method. Cabtaxi(10) was first reported as an upper bound by
Christian Boyer in 2006 and verified as Cabtaxi(10) by
Uwe Hollerbach and reported on the
NMBRTHRY mailing list on May 16, 2008.