Perfect Powers
There are many palindromic perfect powers nk, where n is a natural number and k is 2, 3 or 4.
- Palindromic squares: 0, 1, 4, 9, 121, 484, 676, 10201, 12321, 14641, 40804, 44944, ... (sequence A002779 in OEIS)
- Palindromic cubes: 0, 1, 8, 343, 1331, 1030301, 1367631, 1003003001, ... (sequence A002781 in OEIS)
- Palindromic fourth powers: 0, 1, 14641, 104060401, 1004006004001, ... (sequence A186080 in OEIS)
No palindromes of form n5 (or higher exponent) have been found. The only known non-palindromic number whose cube is a palindrome is 2201.
G. J. Simmons conjectured there are no palindromes of form nk for k > 4.
Read more about this topic: Palindromic Number
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