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What comes next: 2, 1729, 87,539,319, 6,963,472,309,248, ???

The answer, is 48,988,659,276,962,496. What, you didn't get it?

That number is the fifth Taxicab number. The nth Taxicab number is the lowest number that can be expressed as the sum of two cubes in n ways.

Ta(1)=2 - trival
13+13

Ta(2)=1729 - published by Frénicle de Bessy in 1657:
13+1233
93+103

Ta(3)=87539319 - discovered by Leech in 1957
1673+4363
2283+4233
2553+4143

Ta(4)=6963472309248 - discovered by Rosenstiel, Dardis, and Rosenstiel in 1991
24213+190833
54363+189483
102003+180723
133223+166303

Ta(5)=48988659276962496 - discovered by David W. Wilson in 1997
387873+3657573
1078393+3627533
2052923+3429523
2214243+3365883
2315183+3319543

These have become famous because of a certain mathematical incident... G. H. Hardy remembered once going to see Ramanujan in hospital, and had ridden in taxi-cab No. 1729, and remarked to Ramanujan that the number seemed to be rather dull. "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."

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