Editing Palindromic number (section)

===Perfect powers===
There are many palindromic [[perfect power]]s ''n''<sup>''k''</sup>, where ''n'' is a natural number and ''k'' is 2, 3 or 4.
* Palindromic [[Square number|squares]]: 0, 1, 4, 9, 121, 484, 676, 10201, 12321, 14641, 40804, 44944, ... {{OEIS|id=A002779}}
* Palindromic [[Cube (algebra)|cubes]]: 0, 1, 8, 343, 1331, 1030301, 1367631, 1003003001, ... {{OEIS|id=A002781}}
* Palindromic [[fourth power]]s: 0, 1, 14641, 104060401, 1004006004001, ... {{OEIS|id=A186080}}

The first nine terms of the sequence 1<sup>2</sup>, 11<sup>2</sup>, 111<sup>2</sup>, 1111<sup>2</sup>, ... form the palindromes 1, 121, 12321, 1234321, ... {{OEIS|id=A002477}}

The only known non-palindromic number whose cube is a palindrome is 2201, and it is a conjecture the fourth root of all the palindrome fourth powers are a palindrome with 100000...000001 (10<sup>n</sup> + 1).

[[Gustavus Simmons]] conjectured there are no palindromes of form ''n''<sup>''k''</sup> for ''k'' > 4 (and ''n'' > 1).<ref>Murray S. Klamkin (1990), ''Problems in applied mathematics: selections from SIAM review'', [https://books.google.com/books?id=WI9ZGl3M8bYC&pg=PA520 p. 520].</ref>