Strictly non-palindromic number

A strictly non-palindromic number is a natural number, which is a Zahlenpalindrom no priority system, the base is in the range.

The upper limit for the size of the base is necessary in order to maintain the sequence is not trivial, since

  • Any number (greater than 1 ) is written to each base as a one-digit (including palindromic ) number;
  • Any number ( greater than 2), is thus written to the base as a non- palindromic;
  • Any number ( greater than 3 ) is written to the base as ( palindromic ).

For the amount of base is empty, so these numbers are trivially also strictly non- palindromic.

Examples

For example, the ( decimal ) is written the number 6

  • To the base two: 110,
  • To the base three: 20 and
  • To the base four: 12

As none of these spellings is palindromic, 6 is strictly non- palindromic.

The sequence of strictly non-palindromic numbers begins with

Properties

All strictly non-palindromic numbers greater than 6 are prime numbers. For each composite number, a base can be found, to which is palindromic.

Evidence

  • If then, as is what is written in base 2 as 1001 ( palindromic ).
  • If then, as 121 ( palindromic ) is written to the base.

In each case, the base is in the range.

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