A number which declares the amount of digits it contains. more
The first 600 self-describing numbers :
22,
4444,
224444,
442244,
444422,
666666,
10123133,
10123331,
10143133,
10143331,
10153133,
10153331,
10163133,
10163331,
10173133,
10173331,
10183133,
10183331,
10193133,
10193331,
10212332,
10213223,
10232132,
10233221,
10311233,
10311433,
10311533,
10311633,
10311733,
10311833,
10311933,
10313312,
10313314,
10313315,
10313316,
10313317,
10313318,
10313319,
10322123,
10322321,
10331231,
10331431,
10331531,
10331631,
10331731,
10331831,
10331931,
10333112,
10333114,
10333115,
10333116,
10333117,
10333118,
10333119,
12103133,
12103331,
12143133,
12143331,
12153133,
12153331,
12163133,
12163331,
12173133,
12173331,
12183133,
12183331,
12193133,
12193331,
12311033,
12311433,
12311533,
12311633,
12311733,
12311833,
12311933,
12313310,
12313314,
12313315,
12313316,
12313317,
12313318,
12313319,
12331031,
12331431,
12331531,
12331631,
12331731,
12331831,
12331931,
12333110,
12333114,
12333115,
12333116,
12333117,
12333118,
12333119,
14103133,
14103331,
14123133,
14123331,
14153133,
14153331,
14163133,
14163331,
14173133,
14173331,
14183133,
14183331,
14193133,
14193331,
14212332,
14213223,
14232132,
14233221,
14311033,
14311233,
14311533,
14311633,
14311733,
14311833,
14311933,
14313310,
14313312,
14313315,
14313316,
14313317,
14313318,
14313319,
14322123,
14322321,
14331031,
14331231,
14331531,
14331631,
14331731,
14331831,
14331931,
14333110,
14333112,
14333115,
14333116,
14333117,
14333118,
14333119,
15103133,
15103331,
15123133,
15123331,
15143133,
15143331,
15163133,
15163331,
15173133,
15173331,
15183133,
15183331,
15193133,
15193331,
15212332,
15213223,
15232132,
15233221,
15311033,
15311233,
15311433,
15311633,
15311733,
15311833,
15311933,
15313310,
15313312,
15313314,
15313316,
15313317,
15313318,
15313319,
15322123,
15322321,
15331031,
15331231,
15331431,
15331631,
15331731,
15331831,
15331931,
15333110,
15333112,
15333114,
15333116,
15333117,
15333118,
15333119,
16103133,
16103331,
16123133,
16123331,
16143133,
16143331,
16153133,
16153331,
16173133,
16173331,
16183133,
16183331,
16193133,
16193331,
16212332,
16213223,
16232132,
16233221,
16311033,
16311233,
16311433,
16311533,
16311733,
16311833,
16311933,
16313310,
16313312,
16313314,
16313315,
16313317,
16313318,
16313319,
16322123,
16322321,
16331031,
16331231,
16331431,
16331531,
16331731,
16331831,
16331931,
16333110,
16333112,
16333114,
16333115,
16333117,
16333118,
16333119,
17103133,
17103331,
17123133,
17123331,
17143133,
17143331,
17153133,
17153331,
17163133,
17163331,
17183133,
17183331,
17193133,
17193331,
17212332,
17213223,
17232132,
17233221,
17311033,
17311233,
17311433,
17311533,
17311633,
17311833,
17311933,
17313310,
17313312,
17313314,
17313315,
17313316,
17313318,
17313319,
17322123,
17322321,
17331031,
17331231,
17331431,
17331531,
17331631,
17331831,
17331931,
17333110,
17333112,
17333114,
17333115,
17333116,
17333118,
17333119,
18103133,
18103331,
18123133,
18123331,
18143133,
18143331,
18153133,
18153331,
18163133,
18163331,
18173133,
18173331,
18193133,
18193331,
18212332,
18213223,
18232132,
18233221,
18311033,
18311233,
18311433,
18311533,
18311633,
18311733,
18311933,
18313310,
18313312,
18313314,
18313315,
18313316,
18313317,
18313319,
18322123,
18322321,
18331031,
18331231,
18331431,
18331531,
18331631,
18331731,
18331931,
18333110,
18333112,
18333114,
18333115,
18333116,
18333117,
18333119,
19103133,
19103331,
19123133,
19123331,
19143133,
19143331,
19153133,
19153331,
19163133,
19163331,
19173133,
19173331,
19183133,
19183331,
19212332,
19213223,
19232132,
19233221,
19311033,
19311233,
19311433,
19311533,
19311633,
19311733,
19311833,
19313310,
19313312,
19313314,
19313315,
19313316,
19313317,
19313318,
19322123,
19322321,
19331031,
19331231,
19331431,
19331531,
19331631,
19331731,
19331831,
19333110,
19333112,
19333114,
19333115,
19333116,
19333117,
19333118,
20202442,
20203233,
20203332,
20204224,
20242042,
20244220,
20322033,
20323320,
20332032,
20333220,
20422024,
20422420,
21102332,
21103223,
21142332,
21143223,
21152332,
21153223,
21162332,
21163223,
21172332,
21173223,
21182332,
21183223,
21192332,
21193223,
21212442,
21213233,
21213332,
21214224,
21231032,
21231432,
21231532,
21231632,
21231732,
21231832,
21231932,
21233210,
21233214,
21233215,
21233216,
21233217,
21233218,
21233219,
21242142,
21244221,
21321023,
21321423,
21321523,
21321623,
21321723,
21321823,
21321923,
21322133,
21322310,
21322314,
21322315,
21322316,
21322317,
21322318,
21322319,
21323321,
21332132,
21333221,
21422124,
21422421,
22666666,
23102132,
23103221,
23142132,
23143221,
23152132,
23153221,
23162132,
23163221,
23172132,
23173221,
23182132,
23183221,
23192132,
23193221,
23211032,
23211432,
23211532,
23211632,
23211732,
23211832,
23211932,
23213210,
23213214,
23213215,
23213216,
23213217,
23213218,
23213219,
23232442,
23234224,
23242342,
23244223,
23321021,
23321421,
23321521,
23321621,
23321721,
23321821,
23321921,
23322110,
23322114,
23322115,
23322116,
23322117,
23322118,
23322119,
23422324,
23422423,
24202042,
24204220,
24212142,
24214221,
24232342,
24234223,
24243233,
24243332,
24252542,
24254225,
24262642,
24264226,
24272742,
24274227,
24282842,
24284228,
24292942,
24294229,
24322433,
24323324,
24332432,
24333224,
24422020,
24422121,
24422323,
24422525,
24422626,
24422727,
24422828,
24422929,
25242542,
25244225,
25252442,
25253233,
25253332,
25254224,
25322533,
25323325,
25332532,
25333225,
25422425,
25422524,
26242642,
26244226,
26262442,
26263233,
26263332,
26264224,
26322633,
26323326,
26332632,
26333226,
26422426,
26422624,
27242742,
27244227,
27272442,
27273233,
27273332,
27274224,
27322733,
27323327,
27332732,
27333227,
27422427,
27422724,
28242842,
28244228,
28282442,
28283233,
28283332,
28284224,
28322833,
28323328,
28332832,
28333228,
28422428,
28422824,
29242942,
29244229,
29292442,
29293233,
29293332,
29294224,
29322933,
29323329,
29332932,
29333229,
29422429,
29422924,
31101233,
31101433,
31101533,
31101633,
31101733,
31101833,
31101933,
31103312,
31103314,
31103315,
31103316.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 783343 values, from 22 to 88888888666666).
n\r | 0 | 1 |
2 | 339443 | 443900 | 2 |
3 | 259975 | 265258 | 258110 | 3 |
4 | 155477 | 148722 | 183966 | 295178 | 4 |
5 | 149320 | 202255 | 144305 | 150415 | 137048 | 5 |
6 | 111960 | 149474 | 111699 | 148015 | 115784 | 146411 | 6 |
7 | 111488 | 111705 | 112136 | 110476 | 111953 | 111562 | 114023 | 7 |
8 | 74455 | 76347 | 87928 | 137471 | 81022 | 72375 | 96038 | 157707 | 8 |
9 | 96640 | 110964 | 90006 | 84498 | 70061 | 66803 | 78837 | 84233 | 101301 | 9 |
10 | 43990 | 144260 | 100315 | 106330 | 93058 | 105330 | 57995 | 43990 | 44085 | 43990 | 10 |
11 | 77380 | 79155 | 68460 | 61596 | 62202 | 62238 | 68211 | 66330 | 77352 | 82224 | 78195 |
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.