

A001235


Taxicab numbers: sums of 2 cubes in more than 1 way.


111



1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, 373464, 402597, 439101, 443889, 513000, 513856, 515375, 525824, 558441, 593047, 684019, 704977
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OFFSET

1,1


COMMENTS

From Wikipedia: "1729 is known as the HardyRamanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan. In Hardy's words: 'I remember once going to see him when he was 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."'"
A011541 gives another version of "taxicab numbers".
If n is in this sequence, then n*k^3 is also in this sequence for all k > 0. So this sequence is obviously infinite.  Altug Alkan, May 09 2016


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, Section D1.
G. H. Hardy, Ramanujan, Cambridge Univ. Press, 1940, p. 12.
Ya. I. Perelman, Algebra can be fun, pp. 142143.
H. W. Richmond, On integers which satisfy the equation t^3 + x^3 + y^3 + z^3, Trans. Camb. Phil. Soc., 22 (1920), 389403, see p. 402.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 165.


LINKS

A. Grinstein, Ramanujan and 1729, University of Melbourne Dept. of Math and Statistics Newsletter: Issue 3, 1998.


EXAMPLE

4104 belongs to the sequence as 4104 = 2^3 + 16^3 = 9^3 + 15^3.


MATHEMATICA

Select[Range[750000], Length[PowersRepresentations[#, 2, 3]]>1&] (* Harvey P. Dale, Nov 25 2014, with correction by Zak Seidov, Jul 13 2015 *)


PROG

(PARI) is(n)=my(t); for(k=ceil((n/2)^(1/3)), (n.4)^(1/3), if(ispower(nk^3, 3), if(t, return(1), t=1))); 0 \\ Charles R Greathouse IV, Jul 15 2011
(PARI) T=thueinit(x^3+1, 1);


CROSSREFS

Solutions in greater numbers of ways:


KEYWORD

nonn,nice


AUTHOR



STATUS

approved



