|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Nombres SOMME de retournés ou réversibles
Par
exemple, 143 est trois fois somme d'un nombre et de son retourné. Ils
sont très nombreux. Ce sont des palindromes. Intérêts
pour les nombres qui ont au moins deux présentations. |
Anglais: Reversal of a positive integer / digit reversal
|
|
|
|
Lecture: 11 / un seul motif / 11 = 10 + 01 (trivial) 22 / deux motifs / 22 = 11 + 11 = 20 + 02 (triviaux) 55 / trois motifs / 55 = 50 + 05 = 14 + 41 =
23 + 32 198
/ un motif / 198 = 99 + 99 (doublet noté 99) Liste 11,
1, { { 1, 10} } 22,
2, { { 11} , { 2, 20} } 33,
2, { { 3, 30} , { 12, 21} } 44,
3, { { 22} , { 4, 40} , { 13, 31} } 55,
3, { { 5, 50} , { 14, 41} , { 23, 32} } 66,
4, { { 33} , { 6, 60} , { 15, 51} , { 24, 42} } 77,
4, { { 7, 70} , { 16, 61} , { 25, 52} , { 34, 43} } 88,
5, { { 44} , { 8, 80} , { 17, 71} , { 26, 62} , { 35, 53} } 99,
5, { { 9, 90} , { 18, 81} , { 27, 72} , { 36, 63} , { 45, 54} } 101,
1, { { 1, 100} } 110,
5, { { 55} , { 19, 91} , { 28, 82} , { 37, 73} , { 46, 64} } 121,
5, { { 11, 110} , { 29, 92} , { 38, 83} , { 47, 74} , { 56, 65} } 132,
4, { { 66} , { 39, 93} , { 48, 84} , { 57, 75} } 141,
1, { { 21, 120} } 143,
3, { { 49, 94} , { 58, 85} , { 67, 76} } 154,
3, { { 77} , { 59, 95} , { 68, 86} } 161,
1, { { 31, 130} } 165,
2, { { 69, 96} , { 78, 87} } 176,
2, { { 88} , { 79, 97} } 181,
1, { { 41, 140} } 187,
1, { { 89, 98} } 198,
1, { { 99} } 201,
1, { { 51, 150} } 202,
2, { { 101} , { 2, 200} } 221,
1, { { 61, 160} } 222,
2, { { 111} , { 12, 210} } 241,
1, { { 71, 170} } 242,
2, { { 121} , { 22, 220} } 261,
1, { { 81, 180} } 262,
2, { { 131} , { 32, 230} } 281,
1, { { 91, 190} } 282,
2, { { 141} , { 42, 240} } 302,
2, { { 151} , { 52, 250} } 303,
2, { { 3, 300} , { 102, 201} } 322,
2, { { 161} , { 62, 260} } 323,
2, { { 13, 310} , { 112, 211} } 342,
2, { { 171} , { 72, 270} } 343,
2, { { 23, 320} , { 122, 221} } 362,
2, { { 181} , { 82, 280} } 363,
2, { { 33, 330} , { 132, 231} } 382,
2, { { 191} , { 92, 290} } 383,
2, { { 43, 340} , { 142, 241} } 403,
2, { { 53, 350} , { 152, 251} } 404,
3, { { 202} , { 4, 400} , { 103, 301} } 423,
2, { { 63, 360} , { 162, 261} } 424,
3, { { 212} , { 14, 410} , { 113, 311} } 443,
2, { { 73, 370} , { 172, 271} } 444,
3, { { 222} , { 24, 420} , { 123, 321} } 463,
2, { { 83, 380} , { 182, 281} } 464,
3, { { 232} , { 34, 430} , { 133, 331} } 483,
2, { { 93, 390} , { 192, 291} } 484,
3, { { 242} , { 44, 440} , { 143, 341} } 504,
3, { { 252} , { 54, 450} , { 153, 351} } 505,
3, { { 5, 500} , { 104, 401} , { 203, 302} } 524,
3, { { 262} , { 64, 460} , { 163, 361} } 525,
3, { { 15, 510} , { 114, 411} , { 213, 312} } 544,
3, { { 272} , { 74, 470} , { 173, 371} } 545,
3, { { 25, 520} , { 124, 421} , { 223, 322} } 564,
3, { { 282} , { 84, 480} , { 183, 381} } 565,
3, { { 35, 530} , { 134, 431} , { 233, 332} } 584,
3, { { 292} , { 94, 490} , { 193, 391} } 585,
3, { { 45, 540} , { 144, 441} , { 243, 342} } 605,
3, { { 55, 550} , { 154, 451} , { 253, 352} } 606,
4, { { 303} , { 6, 600} , { 105, 501} , { 204, 402} } 625,
3, { { 65, 560} , { 164, 461} , { 263, 362} } 626,
4, { { 313} , { 16, 610} , { 115, 511} , { 214, 412} } 645,
3, { { 75, 570} , { 174, 471} , { 273, 372} } 646,
4, { { 323} , { 26, 620} , { 125, 521} , { 224, 422} } 665,
3, { { 85, 580} , { 184, 481} , { 283, 382} } 666,
4, { { 333} , { 36, 630} , { 135, 531} , { 234, 432} } 685,
3, { { 95, 590} , { 194, 491} , { 293, 392} } 686,
4, { { 343} , { 46, 640} , { 145, 541} , { 244, 442} } 706,
4, { { 353} , { 56, 650} , { 155, 551} , { 254, 452} } 707,
4, { { 7, 700} , { 106, 601} , { 205, 502} , { 304, 403} } 726,
4, { { 363} , { 66, 660} , { 165, 561} , { 264, 462} } 727,
4, { { 17, 710} , { 116, 611} , { 215, 512} , { 314, 413} } 746,
4, { { 373} , { 76, 670} , { 175, 571} , { 274, 472} } 747,
4, { { 27, 720} , { 126, 621} , { 225, 522} , { 324, 423} } 766,
4, { { 383} , { 86, 680} , { 185, 581} , { 284, 482} } 767,
4, { { 37, 730} , { 136, 631} , { 235, 532} , { 334, 433} } 786,
4, { { 393} , { 96, 690} , { 195, 591} , { 294, 492} } 787,
4, { { 47, 740} , { 146, 641} , { 245, 542} , { 344, 443} } 807,
4, { { 57, 750} , { 156, 651} , { 255, 552} , { 354, 453} } 808,
5, { { 404} , { 8, 800} , { 107, 701} , { 206, 602} , { 305, 503} } 827,
4, { { 67, 760} , { 166, 661} , { 265, 562} , { 364, 463} } 828,
5, { { 414} , { 18, 810} , { 117, 711} , { 216, 612} , { 315, 513} } 847,
4, { { 77, 770} , { 176, 671} , { 275, 572} , { 374, 473} } 848,
5, { { 424} , { 28, 820} , { 127, 721} , { 226, 622} , { 325, 523} } 867,
4, { { 87, 780} , { 186, 681} , { 285, 582} , { 384, 483} } 868,
5, { { 434} , { 38, 830} , { 137, 731} , { 236, 632} , { 335, 533} } 887,
4, { { 97, 790} , { 196, 691} , { 295, 592} , { 394, 493} } 888,
5, { { 444} , { 48, 840} , { 147, 741} , { 246, 642} , { 345, 543} } 908,
5, { { 454} , { 58, 850} , { 157, 751} , { 256, 652} , { 355, 553} } 909,
5, { { 9, 900} , { 108, 801} , { 207, 702} , { 306, 603} , { 405, 504} } 928,
5, { { 464} , { 68, 860} , { 167, 761} , { 266, 662} , { 365, 563} } 929,
5, { { 19, 910} , { 118, 811} , { 217, 712} , { 316, 613} , { 415, 514} } 948,
5, { { 474} , { 78, 870} , { 177, 771} , { 276, 672} , { 375, 573} } 949,
5, { { 29, 920} , { 128, 821} , { 227, 722} , { 326, 623} , { 425, 524} } 968,
5, { { 484} , { 88, 880} , { 187, 781} , { 286, 682} , { 385, 583} } 969,
5, { { 39, 930} , { 138, 831} , { 237, 732} , { 336, 633} , { 435, 534} } 988,
5, { { 494} , { 98, 890} , { 197, 791} , { 296, 692} , { 395, 593} } 989,
5, { { 49, 940} , { 148, 841} , { 247, 742} , { 346, 643} , { 445, 544} }
|
|
Voir Tables – Index
|
|
|
|
Records Un
nouveau record est enregistré pour le plus petit nombre ayant plus de motifs
que le nombre tenant le précédent record. Avec
88, on a déjà 5 motifs. Par contre, aucun nombre en centaines n'a plus de 5
motifs. Il attendre 1111 pour obtenir le record suivant avec 6 motifs. Liste 11,
1, {{1, 10}} 22,
2, {{11}, {2, 20}} 44,
3, {{22}, {4, 40}, {13, 31}} 66,
4, {{33}, {6, 60}, {15, 51}, {24, 42}} 88,
5, {{44}, {8, 80}, {17, 71}, {26, 62}, {35, 53}} 1111, 6, {{11, 1100}, {101, 1010}, {209, 902}, {308, 803},
{407, 704}, {506, 605}} 1661,
7, {{61, 1600}, {151, 1510}, {241, 1420}, {331, 1330}, {421, 1240}, {511,
1150}, {601, 1060}} 1771,
8, {{71, 1700}, {161, 1610}, {251, 1520}, {341, 1430}, {431, 1340}, {521,
1250}, {611, 1160}, {701, 1070}} 1881,
9, {{81, 1800}, {171, 1710}, {261, 1620}, {351, 1530}, {441, 1440}, {531,
1350}, {621, 1260}, {711, 1170}, {801, 1080}} 1991,
10, {{91, 1900}, {181, 1810}, {271, 1720}, {361, 1630}, {451, 1540}, {541,
1450}, {631, 1360}, {721, 1270}, {811, 1180}, {901, 1090}} 2662,
11, {{1331}, {62, 2600}, {152, 2510}, {242, 2420}, {332, 2330}, {422, 2240},
{512, 2150}, {602, 2060}, {1061, 1601}, {1151, 1511}, {1241, 1421}} 2772,
12, {{72, 2700}, {162, 2610}, {252, 2520}, {342, 2430}, {432, 2340}, {522,
2250}, {612, 2160}, {702, 2070}, {1071, 1701}, {1161, 1611}, {1251, 1521},
{1341, 1431}} 2882,
14, {{1441}, {82, 2800}, {172, 2710}, {262, 2620}, {352, 2530}, {442, 2440},
{532, 2350}, {622, 2260}, {712, 2170}, {802, 2080}, {1081, 1801}, {1171,
1711}, {1261, 1621}, {1351, 1531}} 2992,
15, {{92, 2900}, {182, 2810}, {272, 2720}, {362, 2630}, {452, 2540}, {542,
2450}, {632, 2360}, {722, 2270}, {812, 2180}, {902, 2090}, {1091, 1901},
{1181, 1811}, {1271, 1721}, {1361, 1631}, {1451, 1541}} 3773,
16, {{73, 3700}, {163, 3610}, {253, 3520}, {343, 3430}, {433, 3340}, {523,
3250}, {613, 3160}, {703, 3070}, {1072, 2701}, {1162, 2611}, {1252, 2521},
{1342, 2431}, {1432, 2341}, {1522, 2251}, {1612, 2161}, {1702, 2071}} 3883,
18, {{83, 3800}, {173, 3710}, {263, 3620}, {353, 3530}, {443, 3440}, {533,
3350}, {623, 3260}, {713, 3170}, {803, 3080}, {1082, 2801}, {1172, 2711},
{1262, 2621}, {1352, 2531}, {1442, 2441}, {1532, 2351}, {1622, 2261}, {1712,
2171}, {1802, 2081}} 3993,
20, {{93, 3900}, {183, 3810}, {273, 3720}, {363, 3630}, {453, 3540}, {543,
3450}, {633, 3360}, {723, 3270}, {813, 3180}, {903, 3090}, {1092, 2901},
{1182, 2811}, {1272, 2721}, {1362, 2631}, {1452, 2541}, {1542, 2451}, {1632,
2361}, {1722, 2271}, {1812, 2181}, {1902, 2091}} 4884,
23, {{2442}, {84, 4800}, {174, 4710}, {264, 4620}, {354, 4530}, {444, 4440},
{534, 4350}, {624, 4260}, {714, 4170}, {804, 4080}, {1083, 3801}, {1173,
3711}, {1263, 3621}, {1353, 3531}, {1443, 3441}, {1533, 3351}, {1623, 3261},
{1713, 3171}, {1803, 3081}, {2082, 2802}, {2172, 2712}, {2262, 2622}, {2352,
2532}} 4994,
25, {{94, 4900}, {184, 4810}, {274, 4720}, {364, 4630}, {454, 4540}, {544,
4450}, {634, 4360}, {724, 4270}, {814, 4180}, {904, 4090}, {1093, 3901},
{1183, 3811}, {1273, 3721}, {1363, 3631}, {1453, 3541}, {1543, 3451}, {1633,
3361}, {1723, 3271}, {1813, 3181}, {1903, 3091}, {2092, 2902}, {2182, 2812},
{2272, 2722}, {2362, 2632}, {2452, 2542}} 5885,
27, {{85, 5800}, {175, 5710}, {265, 5620}, {355, 5530}, {445, 5440}, {535,
5350}, {625, 5260}, {715, 5170}, {805, 5080}, {1084, 4801}, {1174, 4711},
{1264, 4621}, {1354, 4531}, {1444, 4441}, {1534, 4351}, {1624, 4261}, {1714,
4171}, {1804, 4081}, {2083, 3802}, {2173, 3712}, {2263, 3622}, {2353, 3532},
{2443, 3442}, {2533, 3352}, {2623, 3262}, {2713, 3172}, {2803, 3082}} 5995,
30, {{95, 5900}, {185, 5810}, {275, 5720}, {365, 5630}, {455, 5540}, {545,
5450}, {635, 5360}, {725, 5270}, {815, 5180}, {905, 5090}, {1094, 4901},
{1184, 4811}, {1274, 4721}, {1364, 4631}, {1454, 4541}, {1544, 4451}, {1634,
4361}, {1724, 4271}, {1814, 4181}, {1904, 4091}, {2093, 3902}, {2183, 3812},
{2273, 3722}, {2363, 3632}, {2453, 3542}, {2543, 3452}, {2633, 3362}, {2723,
3272}, {2813, 3182}, {2903, 3092}} 6886,
32, {{3443}, {86, 6800}, {176, 6710}, {266, 6620}, {356, 6530}, {446, 6440},
{536, 6350}, {626, 6260}, {716, 6170}, {806, 6080}, {1085, 5801}, {1175,
5711}, {1265, 5621}, {1355, 5531}, {1445, 5441}, {1535, 5351}, {1625, 5261},
{1715, 5171}, {1805, 5081}, {2084, 4802}, {2174, 4712}, {2264, 4622}, {2354,
4532}, {2444, 4442}, {2534, 4352}, {2624, 4262}, {2714, 4172}, {2804, 4082},
{3083, 3803}, {3173, 3713}, {3263, 3623}, {3353, 3533}} 6996,
35, {{96, 6900}, {186, 6810}, {276, 6720}, {366, 6630}, {456, 6540}, {546,
6450}, {636, 6360}, {726, 6270}, {816, 6180}, {906, 6090}, {1095, 5901},
{1185, 5811}, {1275, 5721}, {1365, 5631}, {1455, 5541}, {1545, 5451}, {1635,
5361}, {1725, 5271}, {1815, 5181}, {1905, 5091}, {2094, 4902}, {2184, 4812},
{2274, 4722}, {2364, 4632}, {2454, 4542}, {2544, 4452}, {2634, 4362}, {2724,
4272}, {2814, 4182}, {2904, 4092}, {3093, 3903}, {3183, 3813}, {3273, 3723},
{3363, 3633}, {3453, 3543}} 7887,
36, {{87, 7800}, {177, 7710}, {267, 7620}, {357, 7530}, {447, 7440}, {537, 7350},
{627, 7260}, {717, 7170}, {807, 7080}, {1086, 6801}, {1176, 6711}, {1266,
6621}, {1356, 6531}, {1446, 6441}, {1536, 6351}, {1626, 6261}, {1716, 6171},
{1806, 6081}, {2085, 5802}, {2175, 5712}, {2265, 5622}, {2355, 5532}, {2445,
5442}, {2535, 5352}, {2625, 5262}, {2715, 5172}, {2805, 5082}, {3084, 4803},
{3174, 4713}, {3264, 4623}, {3354, 4533}, {3444, 4443}, {3534, 4353}, {3624,
4263}, {3714, 4173}, {3804, 4083}} 7997,
40, {{97, 7900}, {187, 7810}, {277, 7720}, {367, 7630}, {457, 7540}, {547,
7450}, {637, 7360}, {727, 7270}, {817, 7180}, {907, 7090}, {1096, 6901},
{1186, 6811}, {1276, 6721}, {1366, 6631}, {1456, 6541}, {1546, 6451}, {1636,
6361}, {1726, 6271}, {1816, 6181}, {1906, 6091}, {2095, 5902}, {2185, 5812},
{2275, 5722}, {2365, 5632}, {2455, 5542}, {2545, 5452}, {2635, 5362}, {2725,
5272}, {2815, 5182}, {2905, 5092}, {3094, 4903}, {3184, 4813}, {3274, 4723},
{3364, 4633}, {3454, 4543}, {3544, 4453}, {3634, 4363}, {3724, 4273}, {3814,
4183}, {3904, 4093}} |
|
|
|
||
|
En
prenant un nombre et son retourné, on obtient une infinité de produits, dont
les carrés des nombres. Il n'y a
un intérêt que si un nombre est multi-présentations. Ces cas sont très rares
ou inexistants. |
121
= 11² 252
= 12 x 21 403
= 13 x 31 484
= 22² 574
= 14 x 41 736
= 23 x 32 765
= 15 x 51 976
= 16 x 61 etc. |
|
Voir Nombres
divisible par m et son retourné
|
Suite |
|
|
Voir |
|
|
DicoNombre |
|
|
Site |
|
|
Cette
page |
