The discussion centers on Taxicab numbers, particularly focusing on the structure of these integer sequences. Participants express interest in both the historical context and mathematical properties related to Taxicab numbers, as well as potential avenues for further research.
Participants generally share an interest in Taxicab numbers and their structures, but there is no consensus on the specific resources or methods to explore this topic further. Multiple viewpoints on the relevance of historical context and the utility of OEIS are present.
Some participants express uncertainty regarding the availability of references and the depth of information on the OEIS site, indicating potential limitations in accessing comprehensive resources related to the structure of Taxicab numbers.
Thank you jedishrfu. Yes I had heard a little about that. But to me the taxicab numbers are fascinating in their own right.jedishrfu said:Welcome to PF!
Taxicab numbers are very interesting. There was a recent historical note about them found in Ramanujan's notebooks. Apparently, he was investigating the math surrounding Fermat's Last Theorem:
## a^n + b^n = c^n##
and was collecting them and near misses to study it in the cubic case.
https://phys.org/news/2015-10-mathematicians-magic-key-ramanujan-taxi-cab.html
Did you follow up the references linked on the OEIS page (some of them are paywalled but at least one is free)? By 'follow up' I mean read the linked papers and make sure you understand the relevant parts, then read relevant papers referenced in those papers etc.Larry Lacey said:Yes pbuk, a very good resource on providing the sequence of taxicab numbers but not on the "structure" behind the sequences.