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Message:: [QUOTE="kaparthy, post: 3606262, member: 57463"]Over the past five months, I set aside dollar bills. Today, I entered 166 of them into a spreadsheet to begin THE GREAT TAXICAB SERIAL NUMBER SEARCH. Hardy later retold a story about visiting Ramanujan during his illness:“I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. ‘No,’ he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.’ “As Ramanujan pointed out, 1729 is the smallest number to meet such conditions.  More formally, 1729 = 1^{3} +12^{3} and 1729 = 9^{3} + 10^{3}.  In honor of the Ramanujan-Hardy conversation, the smallest number expressible as the sum of two cubes in n different ways is known as the nth  taxicab number and is denoted as Taxicab (n) .  Therefore, with this notation, we see that Taxicab(2) = 1729 .<a href="https://blogs.ams.org/mathgradblog/2013/08/15/ramanujans-taxicab-number/" target="_blank" class="externalLink ProxyLink" data-proxy-href="https://blogs.ams.org/mathgradblog/2013/08/15/ramanujans-taxicab-number/" rel="nofollow">https://blogs.ams.org/mathgradblog/2013/08/15/ramanujans-taxicab-number/</a> [ATTACH=full]965488[/ATTACH] Well, sure, the last one in this set sorted ascended is 95976588, which, I agree by your story above would be a solutions to (x-95) (x-97) (x-65) (x-88) = 0 or x^4 - 345x^3 +25888x^2 - 447195x + 5469000 = 0or also if you want for (x-9597) (x-6588) = 0and so on... But what I am looking for is intrinsic patterns. What can be said about the digits in 95976588. Do internal relationships exist? Or is something else inherently interesting revealed? First, my interest is personal. If I can find intrinsic patterns in some, a few, or many, I would be satisfied to consider them on their own merits for my own edification. That said, I point out, secondarily, that every popular passion, especially in numismatics, began as someone's personal interest. Q. David Bowers reprinted A Treatise on the Coinage of the United States Branch Mints by   Augustus Goodyear Heaton (1893). Nobody collected by Mint marks back then. (What changed that was the discovery of 1909-S VDB, 484,000 struck versus nearly 28 million Phillies and another 73 million without VDB.) All of the specialties we pursue Early American Copper, Hard Times Tokens, Indian Peace Medals, Inauguration Medals, were all uninteresting until they were popular pursuits. You are right. Most people can understand 10101010 and 15299251 and so on.  Most people  (today) would not care even if you showed them that for 17229584 that 172-squared is 29584. But regardless of what other people do or think, I am interested and that is all that matters to me. [/QUOTE]

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