taxicab numbers
The number has a reputation of its own. The reason is the famous exchange between http://www-groups.dcs.st-and.ac.uk/ history/Mathematicians/Hardy.htmlG. H. Hardy, a famous British mathematician (1877-1947), and http://www-groups.dcs.st-and.ac.uk/ history/Mathematicians/Ramanujan.htmlSrinivasa 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 cabthat had brought him was , which, as numbers go, Hardy thoughtwas “rather a dull number”. At this, Ramanujan perked up, and said“No, it is a very interesting number; it is the smallest numberexpressible 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 theth decimal digit of the transcental number , the next tensuccessive digits of are 0719425863. This is the first appearanceof 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).