A strictly non-palindromic number is an integer n that is not palindromic in any numeral system with a base b in the range 2 ≤ b ≤ n − 2. For example, the number six is written as 110 in base 2, 20 in base 3 and 12 in base 4, none of which is a palindrome—so 6 is strictly non-palindromic.
The sequence of strictly non-palindromic numbers starts:
To test whether a number n is strictly non-palindromic, it must be verified that n is non-palindromic in all bases up to n − 2. The reasons for this upper limit are:
any n ≥ 3 is written 11 in base n − 1, so n is palindromic in base n − 1;
any n ≥ 2 is written 10 in base n, so any n is non-palindromic in base n;
any n ≥ 1 is a single-digit number in any base b > n, so any n is palindromic in all such bases.
Thus it can be seen that the upper limit of n − 2 is necessary to obtain a mathematically 'interesting' definition.
For n < 4 the range of bases is empty, so these numbers are strictly non-palindromic in a trivial way.
Strictly non-palindromic numbers: n is not palindromic in any base b with 2 <= b <= n-2.
Sizlere daha iyi bir deneyim sunabilmek icin sitemizde çerez konumlandırmaktayız, web sitemizi kullanmaya devam ettiğinizde çerezler ile toplanan kişisel verileriniz Veri Politikamız / Bilgilendirmelerimizde belirtilen amaçlar ve yöntemlerle mevzuatına uygun olarak kullanılacaktır.