Cabtaxi Number

The th cabtaxi number is the smallest positive number that can be written in ways as a sum of two (not necessarily positive) cubes. The name derived from the taxicab number, which is the smallest number representable in ways as a sum of positive cubes. The first few are 1, 91, 728, 2741256, 6017193, 1412774811, 11302198488, 137513849003496, 424910390480793000, 933528127886302221000, ... (OEIS A047696), as listed below.

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The 9th term was found by D. Moore (2005) and the 10th by Christian Boyer in 2006, the latter of which was independently verified by Hollerbach (2008).