This discussion centers on Taxicab numbers and their structural properties, particularly in relation to Ramanujan's investigations of Fermat's Last Theorem. Participants highlight the Online Encyclopedia of Integer Sequences (OEIS), specifically entry A011541, as a valuable resource for Taxicab number sequences, although it lacks detailed structural analysis. The conversation emphasizes the importance of exploring linked academic papers for deeper insights into the mathematical underpinnings of these sequences. Users express a desire to connect with the seqfan group for further information and feedback.
PREREQUISITESMathematicians, number theorists, and anyone interested in the structural analysis of integer sequences, particularly those studying Taxicab numbers and their historical context.
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.