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Nombres contenant une
répétition de chiffres de plus en plus grande, suite à une multiplication. Exemple
de motif particulier avec la multiplication par 7 Repdigit qui produit des repdigits partiels |
TABLES pour jusqu'à 100
000
Records du plus petit nombre contenant k fois
le chiffre répété.
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MUL 2 |
Exemple 1665 x 2 = 3330, avec trois
fois le 3 |
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1 |
2 |
3 |
4 |
5 |
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5, 10, 1 55, 110, 2 555, 1110, 3 5555, 11110, 4 55555, 111110, 5 |
1, 2, 1 11, 22, 2 111, 222, 3 1111, 2222, 4 11111, 22222, 5 |
15, 30, 1 165, 330, 2 1665, 3330, 3 16665, 33330, 4 |
2, 4, 1 22, 44, 2 222, 444, 3 2222, 4444, 4 22222, 44444, 5 |
25, 50, 1 275, 550, 2 2775, 5550, 3 27775, 55550, 4 |
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6 |
7 |
8 |
9 |
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3, 6, 1 33, 66, 2 333, 666, 3 3333, 6666, 4 33333, 66666, 5 |
35, 70, 1 385, 770, 2 3885, 7770, 3 38885, 77770, 4 |
4, 8, 1 44, 88, 2 444, 888, 3 4444, 8888, 4 44444, 88888, 5 |
45, 90, 1 495, 990, 2 4995, 9990, 3 49995, 99990, 4 |
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MUL 3 |
Exemple 74 074 x 3 = 222 222, avec
six fois le 3 |
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1 |
2 |
3 |
4 |
5 |
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4, 12, 1 37, 111, 3 3704, 11112, 4 37037, 111111, 6 |
4, 12, 1 74, 222, 3 4074, 12222, 4 74074, 222222, 6 |
1, 3, 1 11, 33, 2 111, 333, 3 1111, 3333, 4 11111, 33333, 5 |
8, 24, 1 48, 144, 2 148, 444, 3 8148, 24444, 4 48148, 144444, 5 |
5, 15, 1 85, 255, 2 185, 555, 3 5185, 15555, 4 85185, 255555, 5 |
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6 |
7 |
8 |
9 |
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2, 6, 1 22, 66, 2 222, 666, 3 2222, 6666, 4 22222, 66666, 5 |
9, 27, 1 59, 177, 2 259, 777, 3 9259, 27777, 4 59259, 177777, 5 |
6, 18, 1 96, 288, 2 296, 888, 3 6296, 18888, 4 96296, 288888, 5 |
3, 9, 1 33, 99, 2 333, 999, 3 3333, 9999, 4 33333, 99999, 5 |
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Dans une colonne, pour MUL 3 comme
pour les autres, les nombres possèdent un air de famille. Normal! Voyez ce cas:
Aucune magie ! 148 est un multiple
de 37 Ce qui conduit à examiner ses
multiples et la production de repdigits. Exemple: 444
= 12 x 37 = 6 x 74 = 3 x 148
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MUL 4 |
Exemple 13 888 x 4 = 55 552, avec
quatre fois le 5 |
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1 |
2 |
3 |
4 |
5 |
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3, 12, 1 28, 112, 2 278, 1112, 3 2778, 11112, 4 27778, 111112, 5 |
3, 12, 1 55, 220, 2 555, 2220, 3 5555, 22220, 4 55555, 222220, 5 |
8, 32, 1 83, 332, 2 833, 3332, 3 8333, 33332, 4 83333, 333332, 5 |
1, 4, 1 11, 44, 2 111, 444, 3 1111, 4444, 4 11111, 44444, 5 |
13, 52, 1 138, 552, 2 1388, 5552, 3 13888, 55552, 4 |
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6 |
7 |
8 |
9 |
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4, 16, 1 165, 660, 2 1665, 6660, 3 16665, 66660, 4 |
18, 72, 1 193, 772, 2 1943, 7772, 3 19443, 77772, 4 |
2, 8, 1 22, 88, 2 222, 888, 3 2222, 8888, 4 22222, 88888, 5 |
23, 92, 1 248, 992, 2 2498, 9992, 3 24998, 99992, 4 |
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MUL 5 |
Exemple 13 332 x 5 = 66 660, avec
quatre fois le 6 |
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1 |
2 |
3 |
4 |
5 |
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2, 10, 1 22, 110, 2 222, 1110, 3 2222, 11110, 4 22222, 111110, 5 |
4, 20, 1 44, 220, 2 444, 2220, 3 4444, 22220, 4 44444, 222220, 5 |
6, 30, 1 66, 330, 2 666, 3330, 3 6666, 33330, 4 66666, 333330, 5 |
8, 40, 1 88, 440, 2 888, 4440, 3 8888, 44440, 4 88888, 444440, 5 |
1, 5, 1 11, 55, 2 111, 555, 3 1111, 5555, 4 11111, 55555, 5 |
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6 |
7 |
8 |
9 |
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12, 60, 1 132, 660, 2 1332, 6660, 3 13332, 66660, 4 |
14, 70, 1 154, 770, 2 1554, 7770, 3 15554, 77770, 4 |
16, 80, 1 176, 880, 2 1776, 8880, 3 17776, 88880, 4 |
18, 90, 1 198, 990, 2 1998, 9990, 3 19998, 99990, 4 |
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MUL 6 |
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1 |
2 |
3 |
4 |
5 |
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2, 12, 1 19, 114, 2 185, 1110, 3 1852, 11112, 4 18519, 111114, 5 |
2, 12, 1 37, 222, 3 2037, 12222, 4 37037, 222222, 6 |
5, 30, 1 55, 330, 2 555, 3330, 3 5555, 33330, 4 55555, 333330, 5 |
4, 24, 1 24, 144, 2 74, 444, 3 4074, 24444, 4 24074, 144444, 5 74074, 444444, 6 |
9, 54, 1 92, 552, 2 925, 5550, 3 9259, 55554, 4 92592, 555552, 5 |
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6 |
7 |
8 |
9 |
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1, 6, 1 11, 66, 2 111, 666, 3 1111, 6666, 4 11111, 66666, 5 |
12, 72, 1 129, 774, 2 1295, 7770, 3 12962, 77772, 4 |
3, 18, 1 48, 288, 2 148, 888, 3 3148, 18888, 4 48148, 288888, 5 |
15, 90, 1 165, 990, 2 1665, 9990, 3 16665, 99990, 4 |
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MUL 7 |
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1 |
2 |
3 |
4 |
5 |
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2, 14, 1 16, 112, 2 159, 1113, 3 1588, 11116, 4 15873, 111111, 6 |
3, 21, 1 32, 224, 2 318, 2226, 3 1746, 12222, 4 31746, 222222, 6 |
5, 35, 1 19, 133, 2 476, 3332, 3 4762, 33334, 4 47619, 333333, 6 |
2, 14, 1 63, 441, 2 492, 3444, 3 3492, 24444, 4 63492, 444444, 6 |
5, 35, 1 65, 455, 2 365, 2555, 3 7936, 55552, 4 79365, 555555, 6 |
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6 |
7 |
8 |
9 |
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8, 56, 1 38, 266, 2 238, 1666, 3 5238, 36666, 4 95238, 666666, 6 |
1, 7, 1 11, 77, 2 111, 777, 3 1111, 7777, 4 11111, 77777, 5 |
4, 28, 1 84, 588, 2 984, 6888, 3 6984, 48888, 4 26984, 188888, 5 |
7, 49, 1 57, 399, 2 857, 5999, 3 2857, 19999, 4 42857, 299999, 5 |
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MUL 8 |
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1 |
2 |
3 |
4 |
5 |
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2, 16, 1 14, 112, 2 139, 1112, 3 1389, 11112, 4 13889, 111112, 5 |
3, 24, 1 28, 224, 2 278, 2224, 3 2778, 22224, 4 27778, 222224, 5 |
4, 32, 1 42, 336, 2 417, 3336, 3 4167, 33336, 4 41667, 333336, 5 |
3, 24, 1 18, 144, 2 555, 4440, 3 5555, 44440, 4 55555, 444440, 5 |
7, 56, 1 69, 552, 2 694, 5552, 3 6944, 55552, 4 69444, 555552, 5 |
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6 |
7 |
8 |
9 |
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2, 16, 1 83, 664, 2 833, 6664, 3 8333, 66664, 4 83333, 666664, 5 |
9, 72, 1 97, 776, 2 972, 7776, 3 9722, 77776, 4 97222, 777776, 5 |
1, 8, 1 11, 88, 2 111, 888, 3 1111, 8888, 4 11111, 88888, 5 |
12, 96, 1 124, 992, 2 1249, 9992, 3 12499, 99992, 4 |
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MUL 9 |
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1 |
2 |
3 |
4 |
5 |
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2, 18, 1 13, 117, 2 124, 1116, 3 1235, 11115, 4 12346, 111114, 5 |
3, 27, 1 25, 225, 2 247, 2223, 3 1358, 12222, 4 24692, 222228, 5 |
37, 333, 3 3704, 33336, 4 37037, 333333, 6 |
5, 45, 1 16, 144, 2 494, 4446, 3 2716, 24444, 4 49383, 444447, 5 |
5, 45, 1 62, 558, 2 395, 3555, 3 6173, 55557, 4 28395, 255555, 5 |
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6 |
7 |
8 |
9 |
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4, 36, 1 74, 666, 3 4074, 36666, 4 74074, 666666, 6 |
3, 27, 1 53, 477, 2 753, 6777, 3 8642, 77778, 4 19753, 177777, 5 |
2, 18, 1 32, 288, 2 432, 3888, 3 5432, 48888, 4 65432, 588888, 5 |
1, 9, 1 11, 99, 2 111, 999, 3 1111, 9999, 4 11111, 99999, 5 |
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