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Mêmes chiffres en décimal et en base b Le
nombre et sa conversion en base b présentent les mêmes chiffres, en même
quantité ou non.
100 + 50 + 8 = 81 + 72 + 5 |
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Nombres
qui comportent les mêmes chiffres dans leur conversion en base b, base allant
de 2 à n – 2. On note de nombreux cas triviaux avec la base
110. |
Exemple 10 en
décimal vaut 1010 en binaire, les deux sont composés de {0 et 1}, mais pas
forcément en même quantité. Autres exemples 2110
= 1219 12210
= 111123 |
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10,
1010, 2 10,
101, 3 13, 31, 4 20, 202,
3 21, 12,
19 23, 32, 7 31, 133,
4 31, 13,
28 41, 14,
37 42, 24,
19 43, 34,
13 46, 64, 7 51, 15,
46 53, 35,
16 61, 16,
55 62, 26,
28 63, 36,
19 71, 17,
64 73, 37,
22 81, 18,
73 82, 28,
37 83, 38,
25 84, 48,
19 86, 68,
13 91, 19,
82 93, 39,
28 100,
1100100, 2 101,
1100101, 2 102,
10210, 3 110,
1101110, 2 112, 12,
110 113, 13,
110 114, 14,
110 115, 15,
110 116, 16,
110 117, 17,
110 118, 18,
110 119, 19,
110 121, 21,
60 121, 12,
119 122,
11112, 3 122, 12,
120 123,
1323, 4 131, 13,
128 133, 31,
44 133, 13,
130 141, 41,
35 141, 14,
137 144, 14,
140 151, 51,
30 151, 15,
146 155, 15,
150 158, 185,
9 161, 16,
155 166, 16,
160 171, 17,
164 |
177, 17,
170 181, 18,
173 188, 18,
180 191, 119,
13 191, 19,
182 196, 169,
11 199, 91,
22 199, 19,
190 200, 20,
100 201,
21110, 3 202, 20,
101 203,
3023, 4 210,
21210, 3 211,
21211, 3 211,
21, 105 211,
12, 209 212,
21212, 3 212, 112,
14 212, 12,
210 213,
1323, 5 220, 20,
110 221, 21,
110 221, 12,
219 222, 22,
110 223, 23,
110 224, 24,
110 225, 25,
110 226, 26,
110 227, 272,
9 227, 27,
110 228, 28,
110 229, 29,
110 231,
3213, 4 233, 32,
77 233, 23,
115 242, 42,
60 242, 24,
119 244, 24,
120 252, 52,
50 255, 25,
125 261, 126,
15 262, 26,
128 265, 526,
7 266, 62,
44 266, 26,
130 277, 27,
135 282, 82,
35 282, 28,
137 283, 238,
11 288, 28,
140 299, 92,
33 299, 29,
145 300, 30,
100 303, 30,
101 311, 13,
308 313, 31,
104 |
313, 13,
310 316, 631,
7 323, 32,
107 323, 23,
160 330, 30,
110 331,
1311, 6 331, 31,
110 331, 13,
328 332, 32,
110 333, 33,
110 334, 34,
110 335, 35,
110 336, 36,
110 337, 37,
110 338, 38,
110 339, 39,
110 343, 43,
85 343, 34,
113 353, 53,
70 353, 35,
116 363, 63,
60 363, 36,
119 366, 36,
120 370, 307,
11 371, 173,
16 373, 37,
122 383, 38,
125 393, 39,
128 399, 93,
44 399, 39,
130 400, 40,
100 404, 40,
101 411, 14,
407 414, 14,
410 422, 42,
105 422, 24,
209 424, 224,
14 424, 24,
210 433, 34,
143 440, 40,
110 441, 144,
19 441, 41,
110 441, 14,
437 442, 42,
110 442, 24,
219 443, 43,
110 444, 44,
110 445, 544,
9 445, 45,
110 446, 46,
110 447, 47,
110 448, 48,
110 449, 49,
110 454, 554,
9 454, 54,
90 466, 64,
77 |
466, 46,
115 484, 84,
60 484, 48,
119 488, 48,
120 499, 94,
55 500, 50,
100 505, 50,
101 511, 115,
22 511, 51,
102 511, 15,
506 515, 15,
510 518, 185,
19 522, 52,
104 525, 25,
260 533, 53,
106 533, 35,
176 544, 455,
11 544, 54,
108 545, 45,
135 550, 50, 110 551, 155,
21 551, 51,
110 551, 15,
546 552, 52,
110 553, 53,
110 554, 54,
110 555, 55,
110 556, 56,
110 557, 57,
110 558, 58,
110 559, 59,
110 566, 56,
112 577, 57,
114 588, 58,
116 599, 95,
66 599, 59,
118 600, 60,
100 606, 60,
101 611, 16,
605 614, 1146,
8 616, 16,
610 622, 26,
308 626, 62,
104 626, 26,
310 633, 63,
105 633, 36,
209 636, 336,
14 636, 36,
210 646, 64,
107 646, 46,
160 656, 56,
130 660, 60,
110 661, 61,
110 661, 16,
655 662, 62,
110 662, 26,
328 |
663, 63,
110 663, 36,
219 664, 64,
110 665, 65,
110 666, 66,
110 667, 67,
110 668, 68,
110 669, 69,
110 686, 86,
85 686, 68,
113 699, 96,
77 699, 69,
115 700, 70,
100 707, 70,
101 711, 17,
704 717, 17,
710 727, 27,
360 733, 37,
242 747, 47,
185 757, 57,
150 770, 70,
110 771, 71,
110 771, 17, 764 772, 72,
110 773, 73,
110 774, 477,
13 774, 74,
110 775, 75,
110 776, 76,
110 777, 77,
110 778, 78,
110 779, 79,
110 782, 278,
18 799, 97,
88 800, 80,
100 801,
1080, 9 808, 80,
101 811, 18,
803 818, 18,
810 822, 28,
407 825, 258,
19 828, 28,
410 833, 38,
275 834, 438,
14 844, 84,
105 844, 48,
209 848, 448,
14 848, 48,
210 858, 58,
170 866, 68,
143 880, 80,
110 881, 81,
110 881, 18,
873 882, 288,
19 882, 82,
110 882, 28,
437 |
883, 83,
110 884, 84,
110 884, 48,
219 885, 85,
110 886, 86,
110 887, 87,
110 888, 88,
110 889, 89,
110 899, 98,
99 900, 90,
100 909, 90,
101 910, 190,
26 911, 191,
26 911, 19,
902 912, 219,
21 912, 192,
26 913, 391,
16 913, 193,
26 914, 194,
26 915, 195,
26 916, 196,
26 917, 197,
26 918, 198,
26 919, 199,
26 919, 91,
102 919, 19, 910 929, 92,
103 929, 29,
460 933, 39,
308 939, 93,
104 939, 39,
310 949, 94,
105 949, 49,
235 958, 589,
13 959, 95,
106 959, 59,
190 961, 169,
28 969, 96,
107 969, 69,
160 979, 97,
108 989, 98,
109 990, 90,
110 991, 91,
110 991, 19,
982 992, 92,
110 993, 93,
110 993, 39,
328 994, 94,
110 995, 95,
110 996, 96,
110 997, 97,
110 998, 98,
110 999, 99,
110 1000,
1111101000, 2 1000,
1101001, 3 |
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Nombres
qui comportent exactement les mêmes chiffres dans leur conversion en base b,
base allant de 2 à n – 2. Ils sont 62 jusqu'à 1000. En italique, chiffres inversés. |
Exemple 13 en décimal
vaut 31 en base 4, les deux sont composés de {0 et 1} en même quantité. Autres exemples 4610
= 647 96110
= 16928 |
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13, 31, 4 21, 12,
19 23, 32, 7 31, 13,
28 41,
14, 37 42,
24, 19 43,
34, 13 46, 64, 7 51, 15,
46 53, 35,
16 61,
16, 55 |
62,
26, 28 63,
36, 19 71, 17,
64 73, 37,
22 81, 18, 73 82, 28, 37 83,
38, 25 84,
48, 19 86, 68,
13 91, 19,
82 93, 39,
28 |
158, 185,
9 191, 119, 13 196, 169,
11 212, 112, 14 227, 272,
9 261, 126,
15 265, 526,
7 283, 238,
11 316, 631,
7 370, 307,
11 |
371, 173,
16 424, 224, 14 441, 144,
19 445, 544,
9 454, 554, 9 511, 115,
22 518, 185,
19 544, 455, 11 551, 155,
21 636, 336, 14 |
774, 477,
13 782, 278,
18 825, 258,
19 834, 438,
14 848, 448, 14 882, 288,
19 910,
190, 26 911,
191, 26 912,
219, 21 912,
192, 26 |
913,
391, 16 913,
193, 26 914,
194, 26 915,
195, 26 916,
196, 26 917,
197, 26 918,
198, 26 919,
199, 26 958, 589,
13 961, 169,
28 |
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Ils sont
90 de 1 000 à 10 000. La base ne dépasse pas 20. |
Exemples 113510
= 51316 123410
= 34127 |
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1030,
3001, 7 1045,
4501, 6 1135,
5131, 6 1234,
3412, 7 1236,
1623, 9 1273,
2371, 8 1366,
3661, 7 1380,
1803, 9 1431,
4113, 7 1454,
4145, 7 1653,
3165, 8 1723,
1327, 11 2027,
2702, 9 2060,
6002, 7 2116,
6112, 7 2154,
4152, 8 2193,
1329, 12 2315,
3152, 9 |
2534,
3425, 9 3160, 6130, 8 3161, 6131, 8 3162, 6132, 8 3163, 6133, 8 3164, 6134, 8 3165, 6135, 8 3166, 6136, 8 3167, 6137, 8 3226,
6232, 8 4063,
3064, 11 4100,
1004, 16 4621,
2146, 13 5141,
1415, 16 5180,
1805, 15 5270,
7205, 9 5272,
2527, 13 5412,
1524, 16 |
5567,
7565, 9 5637,
7653, 9 5657,
7675, 9 5783,
7835, 9 5812,
2851, 13 5920,
2905, 13 6053,
3605, 12 6182,
1826, 16 6572,
2576, 14 7018,
1087, 19 7140, 4170, 12 7141, 4171, 12 7142, 4172, 12 7143, 4173, 12 7144, 4174, 12 7145, 4175, 12 7146, 4176, 12 7147, 4177, 12 |
7148, 4178, 12 7149, 4179, 12 7243,
4237, 12 7364,
3476, 13 7507,
5705, 11 7513,
1537, 18 7587,
5778, 11 7721,
1277, 19 7834,
3748, 13 7873,
3778, 13 7941,
4719, 12 8200,
2008, 16 8461,
1486, 19 8591,
1895, 18 8665,
6568, 11 9143,
3491, 14 9167,
1679, 19 9186,
1689, 19 |
9241,
2419, 16 9304,
4309, 13 9343,
4339, 13 9413,
4391, 13 9471,
1749, 19 9730, 3790, 14 9731, 3791, 14 9732, 3792, 14 9733, 3793, 14 9734, 3794, 14 9735, 3795, 14 9736, 3796, 14 9737, 3797, 14 9738, 3798, 14 9739, 3799, 14 9813,
1839, 19 9825,
5829, 12 9851,
1859, 19 |
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Nombres
dont la valeur dans deux bases comprend les mêmes chiffres exactement. Les occurrences sont très nombreuses. On retrouve
les cas où l'une des base est 10. |
Exemples 710 = 213 = 125 = 2x3+1 = 1x5+2 2310 = 2111 = 1221 = 2x11+1 = 1x21+2 10010
= 9111 = 1991
= 9x11+1 = 1x91+9 |
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7, 21, 3,
12, 5 9, 21, 4,
12, 7 11, 21,
5, 12, 9 13,
31, 4, 13, 10 13,
21, 6, 12, 11 15, 21,
7, 12, 13 16, 31,
5, 13, 13 17, 32,
5, 23, 7 17, 21, 8,
12, 15 19, 31,
6, 13, 16 19, 21,
9, 12, 17 21, 41,
5, 14, 17 21, 21,
10, 12, 19 22,
211, 3, 112, 4 22,
42, 5, 24, 9 22,
31, 7, 13, 19 23, 32,
7, 23, 10 23, 21, 11, 12, 21 25, 221,
3, 121, 4 25, 41,
6, 14, 21 25, 31,
8, 13, 22 25, 21,
12, 12, 23 26, 42, 6,
24, 11 27, 21,
13, 12, 25 28, 130,
4, 103, 5 28, 31,
9, 13, 25 29, 41,
7, 14, 25 29, 32,
9, 23, 13 29, 21,
14, 12, 27 30, 42,
7, 24, 13 31,
51, 6, 15, 26 31,
43, 7, 34, 9 31,
31, 10, 13, 28 31,
21, 15, 12, 29 33, 41,
8, 14, 29 33, 21,
16, 12, 31 34, 42,
8, 24, 15 34, 31,
11, 13, 31 35, 32,
11, 23, 16 35, 21,
17, 12, 33 36, 51,
7, 15, 31 37, 211, 4, 122, 5 37,
52, 7, 25, 16 37,
41, 9, 14, 33 37,
31, 12, 13, 34 37,
21, 18, 12, 35 38, 53,
7, 35, 11 38, 42,
9, 24, 17 39, 21,
19, 12, 37 40, 31,
13, 13, 37 41, 51,
8, 15, 36 41, 41,
10, 14, 37 41, 32,
13, 23, 19 41, 21,
20, 12, 39 42, 42,
10, 24, 19 43, 61,
7, 16, 37 43, 43,
10, 34, 13 43, 31,
14, 13, 40 43, 21, 21, 12, 41 44, 62,
7, 26, 19 45, 63,
7, 36, 13 45, 41, 11, 14, 41 45, 21,
22, 12, 43 46, 141, 5,
114, 6 |
46, 64,
7, 46, 10 46, 51,
9, 15, 41 46, 42,
11, 24, 21 46, 31,
15, 13, 43 47, 52,
9, 25, 21 47, 32,
15, 23, 22 47, 21,
23, 12, 45 49, 61,
8, 16, 43 49, 54,
9, 45, 11 49, 41,
12, 14, 45 49, 31,
16, 13, 46 49, 21,
24, 12, 47 50, 62,
8, 26, 22 50, 42,
12, 24, 23 51, 201,
5, 102, 7 51, 63,
8, 36, 15 51, 51,
10, 15, 46 51, 21,
25, 12, 49 52, 310,
4, 103, 7 52, 31,
17, 13, 49 53, 53,
10, 35, 16 53, 41,
13, 14, 49 53, 32,
17, 23, 25 53, 21,
26, 12, 51 54, 42,
13, 24, 25 55, 313,
4, 131, 6 55, 61, 9,
16, 49 55, 43,
13, 34, 17 55, 31,
18, 13, 52 55, 21,
27, 12, 53 56, 62,
9, 26, 25 56, 51,
11, 15, 51 57, 71,
8, 17, 50 57, 63,
9, 36, 17 57, 52,
11, 25, 26 57, 41,
14, 14, 53 57, 21,
28, 12, 55 58, 64,
9, 46, 13 58, 42,
14, 24, 27 58, 31,
19, 13, 55 59, 32,
19, 23, 28 59, 21,
29, 12, 57 61, 61,
10, 16, 55 61, 51,
12, 15, 56 61, 41,
15, 14, 57 61, 31,
20, 13, 58 61, 21,
30, 12, 59 62, 62,
10, 26, 28 62, 42,
15, 24, 29 63, 63,
10, 36, 19 63, 21,
31, 12, 61 64, 71,
9, 17, 57 64, 31,
21, 13, 61 65, 72, 9,
27, 29 65, 41,
16, 14, 61 65, 32,
21, 23, 31 65, 21,
32, 12, 63 66, 2110, 3, 1002, 4 66, 231,
5, 123, 7 66, 51,
13, 15, 61 66, 42,
16, 24, 31 67,
74, 9, 47, 15 67,
61, 11, 16, 61 |
67,
52, 13, 25, 31 67,
43, 16, 34, 21 67,
31, 22, 13, 64 67,
21, 33, 12, 65 68, 152,
6, 125, 7 68, 62,
11, 26, 31 68, 53,
13, 35, 21 69, 63,
11, 36, 21 69, 54,
13, 45, 16 69, 41,
17, 14, 65 69, 21,
34, 12, 67 70, 64,
11, 46, 16 70, 42,
17, 24, 33 70, 31,
23, 13, 67 71, 71,
10, 17, 64 71, 65,
11, 56, 13 71, 51,
14, 15, 66 71, 32,
23, 23, 34 71, 21,
35, 12, 69 73, 2201, 3, 1021, 4 73, 81,
9, 18, 65 73, 73,
10, 37, 22 73, 61,
12, 16, 67 73, 41,
18, 14, 69 73, 31,
24, 13, 70 73, 21,
36, 12, 71 74, 82,
9, 28, 33 74, 62,
12, 26, 34 74, 42,
18, 24, 35 75, 63,
12, 36, 23 75, 21,
37, 12, 73 76, 84,
9, 48, 17 76, 51,
15, 15, 71 76, 31,
25, 13, 73 77, 52,
15, 25, 36 77, 41,
19, 14, 73 77, 32,
25, 23, 37 77, 21,
38, 12, 75 78, 71, 11, 17, 71 78, 42,
19, 24, 37 79, 72,
11, 27, 36 79, 61,
13, 16, 73 79, 43,
19, 34, 25 79, 31,
26, 13, 76 79, 21,
39, 12, 77 80, 62,
13, 26, 37 81, 81,
10, 18, 73 81, 63,
13, 36, 25 81, 51,
16, 15, 76 81, 41,
20, 14, 77 81, 21,
40, 12, 79 82, 82,
10, 28, 37 82, 75,
11, 57, 15 82, 64,
13, 46, 19 82, 42,
20, 24, 39 82, 31,
27, 13, 79 83, 83,
10, 38, 25 83, 53,
16, 35, 26 83, 32,
27, 23, 40 83, 21,
41, 12, 81 84, 84,
10, 48, 19 85, 71,
12, 17, 78 85, 61,
14, 16, 79 |
85, 41, 21, 14, 81 85, 31,
28, 13, 82 85, 21,
42, 12, 83 86, 86,
10, 68, 13 86, 62,
14, 26, 40 86, 51,
17, 15, 81 86, 42,
21, 24, 41 87, 322,
5, 223, 6 87, 63,
14, 36, 27 87, 52,
17, 25, 41 87, 21,
43, 12, 85 88, 31,
29, 13, 85 89, 81, 11, 18, 81 89, 54,
17, 45, 21 89, 41,
22, 14, 85 89, 32,
29, 23, 43 89, 21,
44, 12, 87 90, 82,
11, 28, 41 90, 42,
22, 24, 43 91, 331,
5, 133, 8 91, 91, 10,
19, 82 91, 61,
15, 16, 85 91, 51,
18, 15, 86 91, 43,
22, 34, 29 91, 31,
30, 13, 88 91, 21,
45, 12, 89 92, 332, 5, 232, 6 92, 84,
11, 48, 21 92, 71,
13, 17, 85 92, 62,
15, 26, 43 93, 93,
10, 39, 28 93, 85,
11, 58, 17 93, 72,
13, 27, 43 93, 63,
15, 36, 29 93, 41,
23, 14, 89 93, 21,
46, 12, 91 94, 163,
7, 136, 8 94, 73,
13, 37, 29 94, 64,
15, 46, 22 94, 42,
23, 24, 45 94, 31,
31, 13, 91 95, 74,
13, 47, 22 95, 32,
31, 23, 46 95, 21,
47, 12, 93 96, 51,
19, 15, 91 97,
81, 12, 18, 89 97,
76, 13, 67, 15 97, 61, 16, 16, 91 97,
52, 19, 25, 46 97,
41, 24, 14, 93 97,
31, 32, 13, 94 97,
21, 48, 12, 95 98, 82,
12, 28, 45 98, 62,
16, 26, 46 98, 53,
19, 35, 31 98, 42,
24, 24, 47 99, 201,
7, 120, 9 99, 71,
14, 17, 92 99, 63,
16, 36, 31 99, 21,
49, 12, 97 100, 91, 11, 19, 91 100, 84,
12, 48, 23 100, 31,
33, 13, 97 |
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Suite |
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Voir |
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Cette page |
http://villemin.gerard.free.fr/Wwwgvmm/Numerati/aaaBASE/MemChiff.htm
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