palindromic number or numeral palindrome is a number that remains the same when its digits are reversed. Like 16461, for example, it is "symmetrical". The term palindromic is derived from palindrome, which refers to a word (such as rotor or racecar) whose spelling is unchanged when its letters are reversed. The first 30 palindromic numbers are:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X, E, 11, 22, 33, 44, 55, 66, 77, 88, 99, XX, EE, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 1X1, 1E1, 202, ...

## Mod n

Pictorial representation of remainders (mod 1, 2, 3, ...,10) frequency for such numbers ≤ 106:

modulo
1 1EEX
2 XXX 1110
3 666 888 888
4 444 666 666 666
5 499 49X 4X7 48E 489
6 222 444 444 444 444 444
7 365 358 345 346 36X 337 345
8 222 333 334 333 222 333 332 333
9 222 2XE 2XE 222 2XE 2XX 222 2XX 2XE
X 225 27X 225 26E 220 274 220 282 220 269
E 222 222 222 222 222 222 222 222 222 222 222
10 0 222 222 222 222 222 222 222 222 222 222 222
remainder 0 1 2 3 4 5 6 7 8 9 X E

A list for how many such numbers ≤ 106 are multiples of the numbers from 1 to 100.

+1 +2 +3 +4 +5 +6 +7 +8 +9 +X +E +10
0+ 1EEX XXX 666 444 499 222 365 222 222 225 222 0
10+ 10XE 171 136 110 149 88 172 X7 E0 E8 105 0
20+ E5 5X5 88 81 104 4E 93 67 70 7X 88 0
30+ 79 88 363 54 69 30 66 48 53 56 60 0
40+ 59 53 46 242 54 2E 55 41 52 54 45 0
50+ 46 40 37 34 270 24 43 31 35 40 3E 0
60+ 40 39 2E 35 3E 121 34 28 2E 32 35 0
70+ 31 31 30 25 52 18 200 23 29 29 44 0
80+ 23 27 25 21 2X 16 26 121 21 24 28 0
90+ 6 26 22 1X 27 18 23 24 121 20 24 0
X0+ 0 21 1X 15 21 10 E 19 19 120 1E 0
E0+ 164 1X 1X 17 1E E 36 19 1X 1E 121 0