A number which remains the same if read backwards. more
The first 600 palindromes :
1,
2,
3,
4,
5,
6,
7,
8,
9,
11,
22,
33,
44,
55,
66,
77,
88,
99,
101,
111,
121,
131,
141,
151,
161,
171,
181,
191,
202,
212,
222,
232,
242,
252,
262,
272,
282,
292,
303,
313,
323,
333,
343,
353,
363,
373,
383,
393,
404,
414,
424,
434,
444,
454,
464,
474,
484,
494,
505,
515,
525,
535,
545,
555,
565,
575,
585,
595,
606,
616,
626,
636,
646,
656,
666,
676,
686,
696,
707,
717,
727,
737,
747,
757,
767,
777,
787,
797,
808,
818,
828,
838,
848,
858,
868,
878,
888,
898,
909,
919,
929,
939,
949,
959,
969,
979,
989,
999,
1001,
1111,
1221,
1331,
1441,
1551,
1661,
1771,
1881,
1991,
2002,
2112,
2222,
2332,
2442,
2552,
2662,
2772,
2882,
2992,
3003,
3113,
3223,
3333,
3443,
3553,
3663,
3773,
3883,
3993,
4004,
4114,
4224,
4334,
4444,
4554,
4664,
4774,
4884,
4994,
5005,
5115,
5225,
5335,
5445,
5555,
5665,
5775,
5885,
5995,
6006,
6116,
6226,
6336,
6446,
6556,
6666,
6776,
6886,
6996,
7007,
7117,
7227,
7337,
7447,
7557,
7667,
7777,
7887,
7997,
8008,
8118,
8228,
8338,
8448,
8558,
8668,
8778,
8888,
8998,
9009,
9119,
9229,
9339,
9449,
9559,
9669,
9779,
9889,
9999,
10001,
10101,
10201,
10301,
10401,
10501,
10601,
10701,
10801,
10901,
11011,
11111,
11211,
11311,
11411,
11511,
11611,
11711,
11811,
11911,
12021,
12121,
12221,
12321,
12421,
12521,
12621,
12721,
12821,
12921,
13031,
13131,
13231,
13331,
13431,
13531,
13631,
13731,
13831,
13931,
14041,
14141,
14241,
14341,
14441,
14541,
14641,
14741,
14841,
14941,
15051,
15151,
15251,
15351,
15451,
15551,
15651,
15751,
15851,
15951,
16061,
16161,
16261,
16361,
16461,
16561,
16661,
16761,
16861,
16961,
17071,
17171,
17271,
17371,
17471,
17571,
17671,
17771,
17871,
17971,
18081,
18181,
18281,
18381,
18481,
18581,
18681,
18781,
18881,
18981,
19091,
19191,
19291,
19391,
19491,
19591,
19691,
19791,
19891,
19991,
20002,
20102,
20202,
20302,
20402,
20502,
20602,
20702,
20802,
20902,
21012,
21112,
21212,
21312,
21412,
21512,
21612,
21712,
21812,
21912,
22022,
22122,
22222,
22322,
22422,
22522,
22622,
22722,
22822,
22922,
23032,
23132,
23232,
23332,
23432,
23532,
23632,
23732,
23832,
23932,
24042,
24142,
24242,
24342,
24442,
24542,
24642,
24742,
24842,
24942,
25052,
25152,
25252,
25352,
25452,
25552,
25652,
25752,
25852,
25952,
26062,
26162,
26262,
26362,
26462,
26562,
26662,
26762,
26862,
26962,
27072,
27172,
27272,
27372,
27472,
27572,
27672,
27772,
27872,
27972,
28082,
28182,
28282,
28382,
28482,
28582,
28682,
28782,
28882,
28982,
29092,
29192,
29292,
29392,
29492,
29592,
29692,
29792,
29892,
29992,
30003,
30103,
30203,
30303,
30403,
30503,
30603,
30703,
30803,
30903,
31013,
31113,
31213,
31313,
31413,
31513,
31613,
31713,
31813,
31913,
32023,
32123,
32223,
32323,
32423,
32523,
32623,
32723,
32823,
32923,
33033,
33133,
33233,
33333,
33433,
33533,
33633,
33733,
33833,
33933,
34043,
34143,
34243,
34343,
34443,
34543,
34643,
34743,
34843,
34943,
35053,
35153,
35253,
35353,
35453,
35553,
35653,
35753,
35853,
35953,
36063,
36163,
36263,
36363,
36463,
36563,
36663,
36763,
36863,
36963,
37073,
37173,
37273,
37373,
37473,
37573,
37673,
37773,
37873,
37973,
38083,
38183,
38283,
38383,
38483,
38583,
38683,
38783,
38883,
38983,
39093,
39193,
39293,
39393,
39493,
39593,
39693,
39793,
39893,
39993,
40004,
40104,
40204,
40304,
40404,
40504,
40604,
40704,
40804,
40904,
41014,
41114,
41214,
41314,
41414,
41514,
41614,
41714,
41814,
41914,
42024,
42124,
42224,
42324,
42424,
42524,
42624,
42724,
42824,
42924,
43034,
43134,
43234,
43334,
43434,
43534,
43634,
43734,
43834,
43934,
44044,
44144,
44244,
44344,
44444,
44544,
44644,
44744,
44844,
44944,
45054,
45154,
45254,
45354,
45454,
45554,
45654,
45754,
45854,
45954,
46064,
46164,
46264,
46364,
46464,
46564,
46664,
46764,
46864,
46964,
47074,
47174,
47274,
47374,
47474,
47574,
47674,
47774,
47874,
47974,
48084,
48184,
48284,
48384,
48484,
48584,
48684,
48784,
48884,
48984,
49094,
49194,
49294,
49394,
49494,
49594,
49694,
49794,
49894,
49994,
50005,
50105.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 109999998 values, from 1 to 999999999999999).
n\r | 0 | 1 |
2 | 48888888 | 61111110 | 2 |
3 | 36666666 | 36666666 | 36666666 | 3 |
4 | 24444444 | 30555555 | 24444444 | 30555555 | 4 |
5 | 12222222 | 24444444 | 24444444 | 24444444 | 24444444 | 5 |
6 | 16296291 | 20370361 | 16296292 | 20370375 | 16296305 | 20370374 | 6 |
7 | 15715310 | 15715536 | 15713032 | 15713079 | 15714841 | 15714984 | 15713216 | 7 |
8 | 12222222 | 15277778 | 12222222 | 15277777 | 12222222 | 15277777 | 12222222 | 15277778 | 8 |
9 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 9 |
10 | 0 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 12222222 | 10 |
11 | 19090907 | 9090910 | 9090909 | 9090909 | 9090909 | 9090909 | 9090909 | 9090909 | 9090909 | 9090909 | 9090909 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.