# [seqfan] Re: Numbers that are the sum of two taxicab numbers in more than one way

franktaw at netscape.net franktaw at netscape.net
Mon Dec 16 16:43:54 CET 2013

```All right, what if we iterate this? Level 1 is the cubes, the smallest
being 1 (or 0, if we allow that).

Level 1 is the taxicab numbers, the smallest being 1729.

Then we have Andrew's sequence, sums of two taxicab numbers  in more
than one way.

Next stop is sums of these numbers in more than one way.

...

Now look for the smallest number at each level:

1, 1729, 485784, ... ?

-----Original Message-----
From: Andrew Weimholt <andrew.weimholt at gmail.com>

The smallest number that is the sum of two taxicab numbers (A001235)
in more than one way is 485784.

439101 + 46683  = 485784
314496 + 171288 = 485784

other examples:

513000 + 4104 = 517104
515375 + 1729 = 517104

443889 + 195841 = 639730
593047 + 46683  = 639730

984067 + 46683  = 1030750
515375 + 515375 = 1030750

984067 + 110656 = 1094723
1080891 + 13832 = 1094723

Sequence starts...

485784, 517104, 639730, 1030750, 1094723, 1127152,
1210813, 1371097, 1395296, 1454355, 1547189, 1574937,
1774297, 1844920, 2102464, 2315131, 2341332, 2411955,
2517424, 2614248, 2738736, 2815155, 2848031, 2989441,
3098368, 3098520, 3508920, 3525704, 3552841, 3886272,
4124729, 4136832, 4144159, 4662441, 4721976, 4782680,
4882176, 4970413, 4980528, 4993352, 5024808, 5046165, ...

Andrew

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```