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Taxicab numbers: Difference between revisions

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Taxicab numbers (view source)

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{{draft task|Mathematics}}
[[File:taxi1729.png|600px||right]]
 
A   [[wp:Hardy–Ramanujan number|taxicab number]]   (the definition that is being used here)  is a positive integer that can be expressed as the sum of two positive cubes in more than one way.
 
The first taxicab number is &nbsp; '''1729''' : 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>
::: <b> <big> 1729 &nbsp; &nbsp; = &nbsp; &nbsp; 1<sup>3</sup> + 12<sup>3</sup> &nbsp; &nbsp; = &nbsp; &nbsp; 9<sup>3</sup> + 10<sup>3</sup> </big> </b>
 
 
;Task requirements
 
* Compute and display the lowest &nbsp; '''25''' &nbsp; taxicab numbers (in numeric order, and in a human-readable format).
* For each of the taxicab numbers, show the number as well as it's constituent cubes.
 
 
;Extra credit:
* Show the &nbsp; 2,000<sup>th</sup> &nbsp; taxicab number, &nbsp; and a half dozen <u>more</u>
 
 
;See also:
* Entry: &nbsp; [http://oeis.org/A001235 A001235 taxicab numbers] on The On-Line Encyclopedia of Integer Sequences.
* Entry: &nbsp; [http://mathworld.wolfram.com/Hardy-RamanujanNumber.html Hardy-Ramanujan Number] on MathWorld.
* Entry: &nbsp; [http://mathworld.wolfram.com/TaxicabNumber.html taxicab number] on MathWorld.
* Entry: &nbsp; [https://en.wikipedia.org/wiki/Taxicab_number taxicab number] on Wikipedia.
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