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A274245 Numbers n such that n*(n+1)/2 is a Taxi-cab number (A001235). 0
349999, 591408, 405332018, 525796270 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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?

A000217(349999) = 61249825000 is the least triangular number that is also a Taxi-cab number.

a(5) > 10^9. - Giovanni Resta, Jul 04 2016

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

349999 is a term because 349999*(349999+1) / 2 = 61249825000 = 820^3 + 3930^3 = 3018^3 + 3232^3.

591408 is a term because 591408*(591408+1) / 2 = 174882006936 = 2070^3 + 5496^3 = 3238^3 + 5204^3.

CROSSREFS

Cf. A000217, A001235.

Sequence in context: A069314 A022208 A213018 * A274254 A122036 A186822

Adjacent sequences: A274242 A274243 A274244 * A274246 A274247 A274248

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Jul 02 2016

EXTENSIONS

a(3)-a(4) from Giovanni Resta, Jul 04 2016

STATUS

approved

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Last modified December 7 12:12 EST 2022. Contains 358656 sequences. (Running on oeis4.)