Palindromic number

A 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