This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274245 #25 Jul 06 2016 01:06:20 %S A274245 349999,591408,405332018,525796270 %N A274245 Numbers n such that n*(n+1)/2 is a Taxi-cab number (A001235). %C A274245 In other words, numbers n such that 0 + 1 + 2 + ... + n = a^3 + b^3 = c^3 + d^3 where (a, b) and (c, d) are distinct pairs and a, b, c, d > 0 is soluble. %C A274245 It is known that there is no triangular number that is also a cube except 0 and 1. So if the sum of k positive cubes is a triangular number that is bigger than 1, then the minimum value of k is 2. At this point sequence focuses on that question: What are the triangular numbers that are the sum of two positive cubes in more than one way? %C A274245 A000217(349999) = 61249825000 is the least triangular number that is also a Taxi-cab number. %C A274245 a(5) > 10^9. - _Giovanni Resta_, Jul 04 2016 %e A274245 349999 is a term because 349999*(349999+1) / 2 = 61249825000 = 820^3 + 3930^3 = 3018^3 + 3232^3. %e A274245 591408 is a term because 591408*(591408+1) / 2 = 174882006936 = 2070^3 + 5496^3 = 3238^3 + 5204^3. %Y A274245 Cf. A000217, A001235. %K A274245 nonn,more %O A274245 1,1 %A A274245 _Altug Alkan_, Jul 02 2016 %E A274245 a(3)-a(4) from _Giovanni Resta_, Jul 04 2016