Talk:Strictly non-palindromic number

Why is 11 listed as a non-palindromic number?


 * Very first sentence of the article: "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." Thus, 11 is strictly non-palindromic if it is non-palindromic in every base between 2 and 9, which it is.  (Every number n is represented as "11" in base n-1, so if we required a strictly non-palindromic number to be non-palindromic in base n-1, e.g., 11 in base 10, no numbers would be strictly non-palindromic.)
 * 11 = 129 = 138 = 147 = 156 = 215 = 234 = 1023 = 10112 Chuck 20:39, 24 August 2006 (UTC)

Why is 10 not a palindromic number?

You can write 010 and this is just the same value! I would like to call numbers like this voluntarily palindromic numbers. After this definition the number 6 will no longer be a strictly non-palindromic number, because in base 2 it is 110 and this is the voluntarily palindromic number 0110. Unsigned
 * Is there any number that is strictly non-palindromic in this stricter definition? Karl 13 Dec 09:55 UT
 * Any n ≥ 2 is written 10 in base n, so any n is the voluntarily palindromic number 010 in base n;
 * If we use the upper limit of n − 2 we'll find the strictly non-palindromic numbers.
 * (I just created the account) Zumthie 23:00, 13 December 2006 (UTC)
 * I now realise that all strictly palindromic numbers other than 6 are strictly palindromic in the new definition, because they are all prime so cannot end in 0 in any applicable base. Karl 09:25 14 December 2006 UT.

Also 4, 4 is 100 in base 2 so you can write "00100". — Preceding unsigned comment added by 101.13.49.41 (talk) 21:13, 21 January 2018 (UTC)

Are there infinitely many strictly non-palindromic numbers?

Up to 100000 I found 1200 strictly non-palindromic prime numbers and these twins: 137          139  4337          4339  8291          8293  9419          9421  10937         10939  13757         13759  19427         19429  20981         20983  36011         36013  38327         38329  43397         43399  59441         59443  71327         71329  74717         74719  76871         76873  90437         90439  91571         91573

Zumthie 06:50, 14 December 2006 (UTC)

Based on the definition given here, shouldn't 4 be the smallest strictly non-palindromic number? This article says that it must be nonpalindromic in all integral bases for 2 ≤ b ≤ n − 2 but for, e.g., n = 0, that would mean 2 ≤ b ≤ -2, which is impossible to satisfy. Only with n ≥ 4 is that definitions possible to satisfy, as 2 ≤ b ≤ n-2 works out to 2 ≤ b ≤ 2 with n=4. Furthermore, 0 and 1 are trivially palindromic (single-digit) in all bases, likewise 2 in all bases ≥ 3, and 3 is palindromic in all bases except base 3 (11 in base-2, single-digit in all bases ≥ 4) XinaNicole (talk) 03:29, 23 May 2018 (UTC)
 * The article notes that the definition is satisfied for n < 4 vacuously: there are no relevant base-b expansions in which those numbers are palindromes, because there are no relevant b at all. Double sharp (talk) 14:22, 20 July 2019 (UTC)