strictly non-palindromic number
If for a given integer there is no base such that each digit of (where is the number of significant digits of in base and is a simple iterator in the range ), meaning that is not a palindromic number in any of these bases, then is called a strictly non-palindromic number.
Clearly will be palindromic for , and though trivially, this is also true for .
6 is the largest composite strictly non-palindromic number. For any other , it is easy to find a base in which is written by simply computing . For odd composites , where is an odd prime and we can almost always either find that for , , or for then and written with two instances of the digit corresponding to in that base. The one odd case of is quickly dismissed with .
|Title||strictly non-palindromic number|
|Date of creation||2013-03-22 16:25:12|
|Last modified on||2013-03-22 16:25:12|
|Last modified by||PrimeFan (13766)|