The palindromic cubes http://oeis.org/A002781
begins 0, 1, 8, 343, 1331, 1030301, ...
Number of ways of representing n as the sum of one or more consecutive primes: http://oeis.org/A054845
Shows one solution for 8 (given) none for 343, one solution for 1331 (as shown by Dej Mar).
There is a table that goes to 10000, which is insufficient for 1030301.
I searched for this a bit with a table of primes. If 1030301 can be written as the sum of consecutive primes, there must be at least 13 of them.
(I also wonder what a trivial case would look like.)
Edited on May 16, 2018, 2:21 pm
Posted by Jer
on 2018-05-16 10:06:09