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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
taxicab numbers
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The number  has a reputation of its own. The reason is the famous exchange between G. H. Hardy, a famous British mathematician (1877-1947), and Srinivasa Ramanujan , one of India's greatest mathematical geniuses (1887-1920):
In 1917, during one visit to Ramanujan in a hospital (he was ill for much of his last three years), Hardy mentioned that the number of the taxi cab that had brought him was  , which, as numbers go, Hardy thought was “rather a dull number”. At this, Ramanujan perked up, and said “No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways.”
Indeed:
Moreover, there are other reasons why  is far from dull.  is the third Carmichael number. Even more strange, beginning at the  th decimal digit of the transcental number  , the next ten successive digits of  are 0719425863. This is the first appearance of all ten digits in a row without repititions.
More generally, the smallest natural number which can be expressed as the sum of  positive cubes is called the  th taxicab number. The first taxicab numbers are:
followed by
 (found by E. Rosenstiel, J.A. Dardis, and C.R. Rosenstiel in 1991) and
 (found by David Wilson on November 21st, 1997).
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"taxicab numbers" is owned by alozano.
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(view preamble)
Cross-references: cubes, positive, sum, natural number, row, digit, even, Carmichael number, Ramanujan, number
There are 4 references to this entry.
This is version 3 of taxicab numbers, born on 2006-03-01, modified 2006-03-02.
Object id is 7664, canonical name is TaxicabNumbers.
Accessed 1258 times total.
Classification:
| AMS MSC: | 00A08 (General :: General and miscellaneous specific topics :: Recreational mathematics) |
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Pending Errata and Addenda
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