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Semiprimi invertibili

Rappresentazione dei numeri 

Si chimano “invertibili” i semiprimi che rimangono tali se letti invertendo l’ordine delle cifre, come 155 = 5 • 31, che diventa 551 = 19 • 29. Normalmente si escludono i semiprimi palindromi.

 

I semiprimi invertibili minori di 1000 (escludendo quelli palindromi) sono: 15, 26, 39, 49, 51, 58, 62, 85, 93, 94, 115, 122, 123, 129, 143, 155, 158, 159, 169, 177, 178, 183, 185, 187, 203, 205, 221, 226, 265, 289, 302, 314, 319, 321, 326, 327, 329, 335, 339, 341, 355, 381, 394, 398, 413, 415, 437, 493, 497, 502, 511, 514, 533, 538, 551, 553, 559, 562, 581, 586, 589, 622, 623, 629, 667, 685, 718, 723, 734, 766, 771, 781, 794, 817, 835, 851, 871, 893, 899, 913, 921, 923, 926, 933, 951, 955, 961, 982, 985, 998.

Qui trovate i semiprimi invertibili fino a 106.

 

Il massimo semiprimo invertibile noto è il prodotto del primo invertibile 105013 + 103296 + 101834 + 1 e del primo palindromo 10200000 + 47960506974 • 1099995 + 1 (Jens Kruse Andersen, 2011, 205014 cifre).

 

Il minimo quadrato magico formato da semiprimi invertibili è il seguente.

3635

7367

2603

3503

4535

5567

6467

1703

5435

 

La definizione può essere estesa ad altre basi; la tabella seguente riporta i semiprimi invertibili fino a 1000 nelle basi fino a 20.

Base

Semiprimi

2

1000112 = 35, 1001102 = 38, 1001112 = 39, 1100012 = 49, 1110012 = 57, 11011112 = 111, 11101102 = 118, 11110112 = 123, 100001012 = 133, 100011012 = 141, 100110112 = 155, 100111102 = 158, 100111112 = 159, 101000012 = 161, 101100012 = 177, 101100102 = 178, 101101112 = 183, 101110112 = 187, 110011102 = 206, 110101112 = 215, 110110012 = 217, 110110102 = 218, 110111012 = 221, 111010112 = 235, 111011012 = 237, 111110012 = 249, 1000010012 = 265, 1000010112 = 267, 1000100102 = 274, 1000101102 = 278, 1000111112 = 287, 1001000012 = 289, 1001000112 = 291, 1001010102 = 298, 1001011012 = 301, 1001011112 = 303, 1001110102 = 314, 1001111112 = 319, 1010001112 = 327, 1010011112 = 335, 1011001102 = 358, 1011010012 = 361, 1011100112 = 371, 1011111102 = 382, 1100001112 = 391, 1100010012 = 393, 1100111012 = 413, 1101000012 = 417, 1101001102 = 422, 1110000112 = 451, 1110001012 = 453, 1110111102 = 478, 1111000102 = 482, 1111001012 = 485, 1111010012 = 489, 1111100012 = 497, 1111110012 = 505, 10000011112 = 527, 10000100012 = 529, 10000111102 = 542, 10000111112 = 543, 10001000012 = 545, 10001001112 = 551, 10001100102 = 562, 10001101012 = 565, 10001111012 = 573, 10010001012 = 581, 10010001112 = 583, 10010010102 = 586, 10010011012 = 589, 10010101012 = 597, 10011000112 = 611, 10011011102 = 622, 10011011112 = 623, 10011101012 = 629, 10011110102 = 634, 10011110112 = 635, 10100010012 = 649, 10100011112 = 655, 10100110112 = 667, 10101001112 = 679, 10101010012 = 681, 10101100012 = 689, 10101101102 = 694, 10101101112 = 695, 10101110012 = 697, 10110000112 = 707, 10110010012 = 713, 10110100112 = 723, 10110111102 = 734, 10111100012 = 753, 10111101102 = 758, 10111110112 = 763, 11000010102 = 778, 11000010112 = 779, 11000011012 = 781, 11000110012 = 793, 11000110102 = 794, 11000111112 = 799, 11001011012 = 813, 11001011112 = 815, 11001111112 = 831, 11010000112 = 835, 11010001102 = 838, 11011001012 = 869, 11011001112 = 871, 11011110012 = 889, 11011111012 = 893, 11100010012 = 905, 11100100012 = 913, 11100100102 = 914, 11100101012 = 917, 11100110112 = 923, 11101001102 = 934, 11101101012 = 949, 11110000012 = 961, 11110001012 = 965, 11110100112 = 979, 11110110012 = 985, 11111000012 = 993, 11111000112 = 995, 11111001102 = 998

3

1123 = 14, 2113 = 22, 10213 = 34, 11023 = 38, 12013 = 46, 12203 = 51, 20113 = 58, 20223 = 62, 22023 = 74, 100203 = 87, 101113 = 94, 111013 = 118, 111123 = 122, 112103 = 129, 121023 = 146, 122023 = 155, 122123 = 158, 201203 = 177, 201213 = 178, 202123 = 185, 202213 = 187, 211113 = 202, 212023 = 209, 212203 = 213, 212213 = 214, 220103 = 219, 1001023 = 254, 1002013 = 262, 1002203 = 267, 1010113 = 274, 1011223 = 287, 1012103 = 291, 1012213 = 295, 1020013 = 298, 1020023 = 299, 1020123 = 302, 1020223 = 305, 1021223 = 314, 1022203 = 321, 1022223 = 323, 1100103 = 327, 1101013 = 334, 1101023 = 335, 1101223 = 341, 1102113 = 346, 1111023 = 362, 1112023 = 371, 1120113 = 382, 1121213 = 394, 1121223 = 395, 1122023 = 398, 1122213 = 403, 1200023 = 407, 1200203 = 411, 1200223 = 413, 1201103 = 417, 1210123 = 437, 1211203 = 447, 1212113 = 454, 1212223 = 458, 1221013 = 469, 1221103 = 471, 1222113 = 481, 2000213 = 493, 2001023 = 497, 2002013 = 505, 2010013 = 514, 2010023 = 515, 2010113 = 517, 2011113 = 526, 2012023 = 533, 2021023 = 551, 2021113 = 553, 2021123 = 554, 2022113 = 562, 2101213 = 583, 2102013 = 586, 2102203 = 591, 2110103 = 597, 2111223 = 611, 2112023 = 614, 2120223 = 629, 2200213 = 655, 2202013 = 667, 2202103 = 669, 2202123 = 671, 2210113 = 679, 2211013 = 685, 2211123 = 689, 2212013 = 694, 2212113 = 697, 2221203 = 717, 2221213 = 718, 2222013 = 721, 2222103 = 723, 10000223 = 737, 10001223 = 746, 10002203 = 753, 10010023 = 758, 10010213 = 763, 10011013 = 766, 10012123 = 779, 10012213 = 781, 10020023 = 785, 10021013 = 793, 10021023 = 794, 10021213 = 799, 10022203 = 807, 10100103 = 813, 10100123 = 815, 10100223 = 818, 10102103 = 831, 10102213 = 835, 10110013 = 838, 10111103 = 849, 10111123 = 851, 10120013 = 865, 10120023 = 866, 10120123 = 869, 10122113 = 886, 10122213 = 889, 10200023 = 893, 10200213 = 898, 10200223 = 899, 10202123 = 914, 10210103 = 921, 10210113 = 922, 10212103 = 939, 10220203 = 951, 10221113 = 958, 10221213 = 961, 11000213 = 979, 11001113 = 985

4

124 = 6, 214 = 9, 10224 = 74, 11024 = 82, 11134 = 87, 12224 = 106, 12334 = 111, 13034 = 115, 13134 = 119, 13234 = 123, 20114 = 133, 20124 = 134, 20324 = 142, 21024 = 146, 22014 = 161, 22214 = 169, 23024 = 178, 30314 = 205, 31114 = 213, 31314 = 221, 32314 = 237, 33214 = 249, 101024 = 274, 102134 = 295, 102314 = 301, 102324 = 302, 102334 = 303, 103224 = 314, 110124 = 326, 110334 = 335, 111034 = 339, 112314 = 365, 113214 = 377, 113314 = 381, 120134 = 391, 120224 = 394, 120234 = 395, 120324 = 398, 121034 = 403, 121234 = 411, 121314 = 413, 121334 = 415, 123114 = 437, 123314 = 445, 130034 = 451, 130124 = 454, 131214 = 473, 132014 = 481, 132114 = 485, 133114 = 501, 133214 = 505, 200324 = 526, 201014 = 529, 202134 = 551, 202224 = 554, 203124 = 566, 210114 = 581, 210134 = 583, 210314 = 589, 212334 = 623, 213024 = 626, 213224 = 634, 220214 = 649, 221234 = 667, 222024 = 674, 223014 = 689, 223124 = 694, 223334 = 703, 230024 = 706, 230214 = 713, 231234 = 731, 232014 = 737, 233234 = 763, 300234 = 779, 300314 = 781, 301114 = 789, 301134 = 791, 301214 = 793, 301334 = 799, 302334 = 815, 303334 = 831, 310124 = 838, 310214 = 841, 311034 = 851, 312014 = 865, 312024 = 866, 320034 = 899, 320214 = 905, 321214 = 921, 321224 = 922, 321324 = 926, 322334 = 943, 323324 = 958, 330114 = 965, 331034 = 979, 331214 = 985, 332014 = 993, 332034 = 995, 332124 = 998

5

145 = 9, 245 = 14, 415 = 21, 425 = 22, 1145 = 34, 1235 = 38, 1245 = 39, 1445 = 49, 2135 = 58, 2445 = 74, 3125 = 82, 3215 = 86, 3345 = 94, 4115 = 106, 4215 = 111, 4335 = 118, 4415 = 121, 4425 = 122, 10045 = 129, 10145 = 134, 10315 = 141, 10325 = 142, 10335 = 143, 10415 = 146, 11315 = 166, 11345 = 169, 12035 = 178, 12135 = 183, 12345 = 194, 13015 = 201, 13035 = 203, 13115 = 206, 13245 = 214, 13305 = 215, 13325 = 217, 13335 = 218, 13345 = 219, 14015 = 226, 14225 = 237, 14425 = 247, 20035 = 253, 20045 = 254, 20145 = 259, 20225 = 262, 20305 = 265, 20325 = 267, 21035 = 278, 21435 = 298, 22025 = 302, 22145 = 309, 22245 = 314, 22415 = 321, 23015 = 326, 23025 = 327, 23045 = 329, 23145 = 334, 23315 = 341, 24135 = 358, 24415 = 371, 30025 = 377, 30125 = 382, 30215 = 386, 30315 = 391, 30335 = 393, 30435 = 398, 31215 = 411, 31425 = 422, 33015 = 451, 33035 = 453, 33315 = 466, 33435 = 473, 34035 = 478, 34125 = 482, 34245 = 489, 34335 = 493, 40015 = 501, 40025 = 502, 40245 = 514, 40325 = 517, 40345 = 519, 41015 = 526, 41025 = 527, 41225 = 537, 41325 = 542, 42045 = 554, 42225 = 562, 42315 = 566, 42435 = 573, 43045 = 579, 43115 = 581, 43215 = 586, 43315 = 591, 100045 = 629, 101325 = 667, 101345 = 669, 102205 = 685, 102405 = 695, 102435 = 698, 103235 = 713, 103335 = 718, 104115 = 731, 104415 = 746, 104445 = 749, 110315 = 766, 110325 = 767, 111035 = 778, 111345 = 794, 111445 = 799, 112025 = 802, 112235 = 813, 112325 = 817, 112335 = 818, 113235 = 838, 113315 = 841, 113325 = 842, 114015 = 851, 114305 = 865, 114345 = 869, 120245 = 889, 120405 = 895, 120435 = 898, 121105 = 905, 121325 = 917, 122245 = 939, 123435 = 973, 123445 = 974, 124045 = 979, 124125 = 982, 124205 = 985, 124335 = 993, 124405 = 995

6

146 = 10, 416 = 25, 1236 = 51, 1456 = 65, 2236 = 87, 3216 = 121, 3226 = 122, 3546 = 142, 3556 = 143, 4536 = 177, 5416 = 205, 5536 = 213, 10036 = 219, 10056 = 221, 10146 = 226, 11216 = 265, 11346 = 274, 11426 = 278, 11556 = 287, 12116 = 295, 12146 = 298, 12226 = 302, 12256 = 305, 12426 = 314, 12536 = 321, 12556 = 323, 13026 = 326, 13036 = 327, 13056 = 329, 13156 = 335, 13516 = 355, 14156 = 371, 14256 = 377, 14336 = 381, 14556 = 395, 15156 = 407, 15316 = 415, 20056 = 437, 20316 = 451, 20336 = 453, 20346 = 454, 20546 = 466, 22146 = 514, 22216 = 517, 22236 = 519, 22356 = 527, 22456 = 533, 22536 = 537, 24036 = 579, 24116 = 583, 24146 = 586, 24216 = 589, 24236 = 591, 24556 = 611, 30016 = 649, 30316 = 667, 30356 = 671, 30426 = 674, 30536 = 681, 32226 = 734, 32256 = 737, 32426 = 746, 32536 = 753, 33026 = 758, 33146 = 766, 33156 = 767, 33346 = 778, 33416 = 781, 33536 = 789, 35036 = 831, 35146 = 838, 35216 = 841, 35226 = 842, 35236 = 843, 35336 = 849, 35546 = 862, 41016 = 901, 41216 = 913, 41226 = 914, 41336 = 921, 41346 = 922, 41356 = 923, 41426 = 926, 41536 = 933, 43026 = 974, 43116 = 979, 43146 = 982, 43256 = 989, 43336 = 993

7

127 = 9, 137 = 10, 217 = 15, 317 = 22, 357 = 26, 457 = 33, 467 = 34, 537 = 38, 547 = 39, 647 = 46, 1067 = 55, 1127 = 58, 1167 = 62, 1267 = 69, 1347 = 74, 1457 = 82, 1527 = 86, 1537 = 87, 1627 = 93, 2117 = 106, 2167 = 111, 2347 = 123, 2437 = 129, 2517 = 134, 2617 = 141, 2657 = 145, 3147 = 158, 3257 = 166, 3427 = 177, 3517 = 183, 4057 = 201, 4067 = 202, 4137 = 206, 4167 = 209, 4307 = 217, 4317 = 218, 4327 = 219, 5047 = 249, 5237 = 262, 5417 = 274, 5627 = 289, 6017 = 295, 6047 = 298, 6117 = 302, 6127 = 303, 6147 = 305, 6217 = 309, 10157 = 355, 10257 = 362, 10547 = 382, 10667 = 391, 11027 = 394, 11037 = 395, 11067 = 398, 11257 = 411, 11307 = 413, 11327 = 415, 11347 = 417, 11507 = 427, 12047 = 445, 12067 = 447, 12157 = 453, 12167 = 454, 12237 = 458, 12627 = 485, 13307 = 511, 13337 = 514, 13347 = 515, 13367 = 517, 13547 = 529, 13637 = 535, 13657 = 537, 13667 = 538, 14047 = 543, 14157 = 551, 14327 = 562, 14357 = 565, 14367 = 566, 14467 = 573, 14607 = 581, 14657 = 586, 15127 = 597, 15327 = 611, 15657 = 635, 16157 = 649, 16247 = 655, 16527 = 674, 16667 = 685, 20117 = 694, 20127 = 695, 20157 = 698, 20437 = 717, 20507 = 721, 20527 = 723, 21027 = 737, 21267 = 755, 21327 = 758, 21407 = 763, 21437 = 766, 21447 = 767, 21517 = 771, 21627 = 779, 22057 = 789, 22107 = 791, 22137 = 794, 22247 = 802, 22257 = 803, 22327 = 807, 22437 = 815, 22457 = 817, 23117 = 841, 23127 = 842, 23137 = 843, 23227 = 849, 23417 = 862, 23447 = 865, 23457 = 866, 23517 = 869, 23637 = 878, 23647 = 879, 24047 = 886, 24237 = 899, 24257 = 901, 24437 = 913, 25027 = 933, 25247 = 949, 25467 = 965, 25617 = 974, 26127 = 989, 26217 = 995, 26247 = 998

8

168 = 14, 178 = 15, 618 = 49, 678 = 55, 718 = 57, 768 = 62, 1058 = 69, 1158 = 77, 1228 = 82, 1338 = 91, 1378 = 95, 1528 = 106, 1578 = 111, 1678 = 119, 1728 = 122, 1738 = 123, 2068 = 134, 2168 = 142, 2178 = 143, 2218 = 145, 2338 = 155, 2518 = 169, 2718 = 185, 3168 = 206, 3258 = 213, 3268 = 214, 3318 = 217, 3328 = 218, 3718 = 249, 5018 = 321, 5078 = 327, 5118 = 329, 5238 = 339, 5768 = 382, 6028 = 386, 6078 = 391, 6128 = 394, 6138 = 395, 6238 = 403, 6378 = 415, 6758 = 445, 7058 = 453, 7068 = 454, 7128 = 458, 7318 = 473, 7368 = 478, 7518 = 489, 7618 = 497, 10038 = 515, 10058 = 517, 10178 = 527, 10278 = 535, 10368 = 542, 10378 = 543, 10478 = 551, 10528 = 554, 11058 = 581, 11468 = 614, 11568 = 622, 11628 = 626, 12178 = 655, 12338 = 667, 12518 = 681, 12578 = 687, 12618 = 689, 12668 = 694, 12678 = 695, 13038 = 707, 13158 = 717, 13168 = 718, 13238 = 723, 13418 = 737, 13528 = 746, 13618 = 753, 13638 = 755, 13668 = 758, 13768 = 766, 14038 = 771, 14128 = 778, 14138 = 779, 14258 = 789, 14318 = 793, 14378 = 799, 14428 = 802, 14478 = 807, 14558 = 813, 14578 = 815, 14628 = 818, 15038 = 835, 15068 = 838, 15138 = 843, 15218 = 849, 15368 = 862, 15668 = 886, 16028 = 898, 16038 = 899, 16218 = 913, 16318 = 921, 16468 = 934, 16578 = 943, 16658 = 949, 16738 = 955, 16768 = 958, 17158 = 973, 17168 = 974, 17358 = 989, 17438 = 995, 17468 = 998

9

159 = 14, 169 = 15, 249 = 22, 279 = 25, 289 = 26, 369 = 33, 429 = 38, 519 = 46, 619 = 55, 639 = 57, 729 = 65, 829 = 74, 1139 = 93, 1149 = 94, 1159 = 95, 1279 = 106, 1449 = 121, 1539 = 129, 1589 = 134, 1679 = 142, 1689 = 143, 1729 = 146, 1829 = 155, 1859 = 158, 1869 = 159, 1889 = 161, 2049 = 166, 2169 = 177, 2449 = 202, 2569 = 213, 2579 = 214, 2589 = 215, 2639 = 219, 2719 = 226, 2819 = 235, 3049 = 247, 3069 = 249, 3119 = 253, 3179 = 259, 3489 = 287, 3519 = 289, 3629 = 299, 3649 = 301, 3669 = 303, 3889 = 323, 4029 = 326, 4039 = 327, 4119 = 334, 4419 = 361, 4429 = 362, 4459 = 365, 4589 = 377, 4639 = 381, 4689 = 386, 4769 = 393, 4779 = 394, 5119 = 415, 5189 = 422, 5449 = 445, 5469 = 447, 5589 = 458, 5679 = 466, 5819 = 478, 6039 = 489, 6079 = 493, 6129 = 497, 6279 = 511, 6459 = 527, 6529 = 533, 6639 = 543, 6749 = 553, 6819 = 559, 7069 = 573, 7139 = 579, 7219 = 586, 7269 = 591, 7529 = 614, 7619 = 622, 7659 = 626, 7749 = 634, 8159 = 662, 8439 = 687, 8519 = 694, 8529 = 695, 8549 = 697, 8559 = 698, 8619 = 703, 8649 = 706, 8819 = 721, 8839 = 723, 10059 = 734, 10089 = 737, 10189 = 746, 10269 = 753, 10469 = 771, 10579 = 781, 10629 = 785, 10689 = 791, 10729 = 794, 10779 = 799, 11239 = 831, 11319 = 838, 11359 = 842, 11369 = 843, 11459 = 851, 11629 = 866, 11659 = 869, 11679 = 871, 11759 = 878, 11849 = 886, 11879 = 889, 12029 = 893, 12049 = 895, 12249 = 913, 12259 = 914, 12289 = 917, 12339 = 921, 12469 = 933, 12539 = 939, 12649 = 949, 12719 = 955, 13029 = 974, 13079 = 979, 13119 = 982, 13189 = 989, 13289 = 998

10

15, 26, 39, 49, 51, 58, 62, 85, 93, 94, 115, 122, 123, 129, 143, 155, 158, 159, 169, 177, 178, 183, 185, 187, 203, 205, 221, 226, 265, 289, 302, 314, 319, 321, 326, 327, 329, 335, 339, 341, 355, 381, 394, 398, 413, 415, 437, 493, 497, 502, 511, 514, 533, 538, 551, 553, 559, 562, 581, 586, 589, 622, 623, 629, 667, 685, 718, 723, 734, 766, 771, 781, 794, 817, 835, 851, 871, 893, 899, 913, 921, 923, 926, 933, 951, 955, 961, 982, 985, 998

11

1311 = 14, 1A11 = 21, 2311 = 25, 2411 = 26, 3111 = 34, 3211 = 35, 3511 = 38, 3611 = 39, 4211 = 46, 5311 = 58, 5711 = 62, 5A11 = 65, 6311 = 69, 6811 = 74, 7511 = 82, 7811 = 85, 7911 = 86, 8611 = 94, 8711 = 95, 9711 = 106, A111 = 111, A511 = 115, 11211 = 134, 11911 = 141, 12211 = 145, 12311 = 146, 14411 = 169, 15211 = 178, 15911 = 185, 16711 = 194, 17411 = 202, 17811 = 206, 18411 = 213, 18511 = 214, 18611 = 215, 18811 = 217, 18A11 = 219, 20711 = 249, 21111 = 254, 22111 = 265, 22A11 = 274, 23311 = 278, 24911 = 295, 25111 = 298, 25511 = 302, 26611 = 314, 27711 = 326, 27811 = 327, 28511 = 335, 29511 = 346, 2A611 = 358, 2AA11 = 362, 31811 = 382, 32111 = 386, 32811 = 393, 32911 = 394, 33211 = 398, 34A11 = 417, 35411 = 422, 35911 = 427, 36811 = 437, 37511 = 445, 38011 = 451, 39411 = 466, 39711 = 469, 39911 = 471, 3A511 = 478, 3A811 = 481, 3A911 = 482, 41711 = 502, 42911 = 515, 43911 = 526, 43A11 = 527, 44111 = 529, 44711 = 535, 44911 = 537, 45311 = 542, 45611 = 545, 46911 = 559, 47111 = 562, 48111 = 573, 48711 = 579, 49311 = 586, 50611 = 611, 50911 = 614, 51A11 = 626, 52611 = 633, 52811 = 635, 54011 = 649, 55211 = 662, 55911 = 669, 57311 = 685, 58111 = 694, 58211 = 695, 59211 = 706, 5A311 = 718, 5A611 = 721, 60511 = 731, 60811 = 734, 61811 = 745, 62511 = 753, 62A11 = 758, 63711 = 766, 63811 = 767, 64811 = 778, 64911 = 779, 65411 = 785, 65A11 = 791, 66211 = 794, 66A11 = 802, 67A11 = 813, 68111 = 815, 69A11 = 835, 6A211 = 838, 6A511 = 841, 70211 = 849, 71411 = 862, 73611 = 886, 74411 = 895, 74A11 = 901, 76111 = 914, 76811 = 921, 77211 = 926, 77A11 = 934, 78411 = 939, 79311 = 949, 79911 = 955, 80611 = 974, 81311 = 982, 81611 = 985, 82311 = 993, 82511 = 995

12

1212 = 14, 1A12 = 22, 2112 = 25, 2A12 = 34, 2B12 = 35, 3A12 = 46, 7912 = 93, 9712 = 115, 9A12 = 118, 9B12 = 119, A112 = 121, A212 = 122, A312 = 123, A912 = 129, B212 = 134, B912 = 141, 10212 = 146, 10B12 = 155, 11212 = 158, 11312 = 159, 12A12 = 178, 13312 = 183, 14912 = 201, 14B12 = 203, 15512 = 209, 15912 = 213, 15A12 = 214, 16212 = 218, 16312 = 219, 16512 = 221, 16A12 = 226, 18912 = 249, 1A312 = 267, 1AA12 = 274, 1BB12 = 287, 20112 = 289, 21112 = 301, 21312 = 303, 21512 = 305, 22912 = 321, 23512 = 329, 23A12 = 334, 23B12 = 335, 24312 = 339, 25A12 = 358, 26112 = 361, 26512 = 365, 26B12 = 371, 27912 = 381, 28A12 = 394, 2A312 = 411, 2A512 = 413, 2A912 = 417, 2B712 = 427, 30512 = 437, 31112 = 445, 31212 = 446, 33112 = 469, 34212 = 482, 34512 = 485, 34912 = 489, 36112 = 505, 37A12 = 526, 37B12 = 527, 39512 = 545, 3A112 = 553, 3A212 = 554, 3AA12 = 562, 50312 = 723, 50B12 = 731, 51212 = 734, 53212 = 758, 54312 = 771, 55112 = 781, 55B12 = 791, 56112 = 793, 56212 = 794, 56A12 = 802, 56B12 = 803, 57912 = 813, 57B12 = 815, 59312 = 831, 59712 = 835, 5A212 = 842, 5BA12 = 862

13

1913 = 22, 2713 = 33, 2813 = 34, 2913 = 35, 2C13 = 38, 3713 = 46, 3A13 = 49, 3C13 = 51, 4513 = 57, 4613 = 58, 4A13 = 62, 5413 = 69, 5913 = 74, 5C13 = 77, 6413 = 82, 6913 = 87, 7213 = 93, 7313 = 94, 8213 = 106, 9113 = 118, 9213 = 119, 9513 = 122, 9613 = 123, A313 = 133, A413 = 134, AC13 = 142, C213 = 158, C313 = 159, C513 = 161, CA13 = 166, 10913 = 178, 11C13 = 194, 12613 = 201, 12813 = 203, 12A13 = 205, 13913 = 217, 14513 = 226, 15313 = 237, 16213 = 249, 16713 = 254, 19913 = 295, 1A213 = 301, 1A413 = 303, 1A613 = 305, 1AA13 = 309, 1B213 = 314, 1C913 = 334, 20813 = 346, 21713 = 358, 21B13 = 362, 22713 = 371, 23413 = 381, 23513 = 382, 24513 = 395, 25A13 = 413, 25C13 = 415, 26113 = 417, 26613 = 422, 26B13 = 427, 28513 = 447, 29313 = 458, 2A113 = 469, 2AA13 = 478, 2B013 = 481, 2B113 = 482, 2B813 = 489, 2BC13 = 493, 30413 = 511, 30713 = 514, 30813 = 515, 30C13 = 519, 31713 = 527, 31913 = 529, 34013 = 559, 34713 = 566, 35113 = 573, 35913 = 581, 35B13 = 583, 38B13 = 622, 39213 = 626, 39513 = 629, 39913 = 633, 3BC13 = 662, 3C413 = 667, 3CB13 = 674, 40313 = 679, 40513 = 681, 41513 = 694, 41813 = 697, 41913 = 698, 41A13 = 699, 43213 = 717, 43613 = 721, 44913 = 737, 45513 = 746, 46913 = 763, 47013 = 767, 47B13 = 778, 47C13 = 779, 48B13 = 791, 49013 = 793, 49613 = 799, 49913 = 802, 4A113 = 807, 4A713 = 813, 4A913 = 815, 4C313 = 835, 4C613 = 838, 4C913 = 841, 4CB13 = 843, 50413 = 849, 51413 = 862, 52713 = 878, 52813 = 879, 53213 = 886, 53913 = 893, 53B13 = 895, 54113 = 898, 54213 = 899, 55413 = 914, 55713 = 917, 55B13 = 921, 55C13 = 922, 56B13 = 934, 58213 = 951, 58A13 = 959, 59313 = 965, 59B13 = 973, 5A713 = 982, 5BA13 = 998

14

1B14 = 25, 1C14 = 26, 2614 = 34, 2A14 = 38, 3914 = 51, 3D14 = 55, 6214 = 86, 6A14 = 94, 7814 = 106, 8714 = 119, 8914 = 121, 9314 = 129, 9814 = 134, A214 = 142, A614 = 146, B114 = 155, C114 = 169, D314 = 185, 10614 = 202, 10914 = 205, 10A14 = 206, 11414 = 214, 11514 = 215, 11714 = 217, 11914 = 219, 11B14 = 221, 12D14 = 237, 13914 = 247, 13B14 = 249, 14D14 = 265, 15814 = 274, 16714 = 287, 16914 = 289, 17514 = 299, 18D14 = 321, 19C14 = 334, 1A514 = 341, 1AA14 = 346, 1B514 = 355, 1BC14 = 362, 1C714 = 371, 1D314 = 381, 1D814 = 386, 22714 = 427, 24614 = 454, 24A14 = 458, 26614 = 482, 28714 = 511, 2A614 = 538, 2AA14 = 542, 2C614 = 566, 31914 = 611, 31C14 = 614, 32614 = 622, 32714 = 623, 32A14 = 626, 34B14 = 655, 35914 = 667, 35B14 = 669, 36914 = 681, 37914 = 695, 37B14 = 697, 37C14 = 698, 37D14 = 699, 39414 = 718, 39714 = 721, 39914 = 723, 3B714 = 749, 3BD14 = 755, 3CB14 = 767, 3D114 = 771, 41114 = 799, 41514 = 803, 45814 = 862, 45C14 = 866, 47B14 = 893, 49314 = 913, 49714 = 917, 4B514 = 943, 4D814 = 974, 4DD14 = 979, 50914 = 989, 51114 = 995, 51414 = 998

15

1615 = 21, 1715 = 22, 1B15 = 26, 2415 = 34, 2515 = 35, 2815 = 38, 3615 = 51, 3C15 = 57, 4215 = 62, 4E15 = 74, 5215 = 77, 5A15 = 85, 5C15 = 87, 6115 = 91, 6315 = 93, 7115 = 106, 7D15 = 118, 7E15 = 119, 8215 = 122, 8915 = 129, 8D15 = 133, 8E15 = 134, 9815 = 143, 9A15 = 145, A515 = 155, A915 = 159, B115 = 166, BD15 = 178, C315 = 183, C515 = 185, D715 = 202, D815 = 203, DB15 = 206, E415 = 214, E715 = 217, E815 = 218, 10C15 = 237, 11715 = 247, 11915 = 249, 11D15 = 253, 11E15 = 254, 14215 = 287, 14415 = 289, 14615 = 291, 14D15 = 298, 15215 = 302, 15915 = 309, 15E15 = 314, 16615 = 321, 16815 = 323, 16B15 = 326, 16E15 = 329, 17415 = 334, 17B15 = 341, 18D15 = 358, 19215 = 362, 19515 = 365, 19B15 = 371, 1A615 = 381, 1A715 = 382, 1B315 = 393, 1B815 = 398, 1BD15 = 403, 1C815 = 413, 1CC15 = 417, 1EA15 = 445, 1EC15 = 447, 21415 = 469, 21815 = 473, 21D15 = 478, 22515 = 485, 23615 = 501, 23715 = 502, 24115 = 511, 25115 = 526, 25A15 = 535, 26315 = 543, 26B15 = 551, 26D15 = 553, 26E15 = 554, 27415 = 559, 27B15 = 566, 28915 = 579, 28D15 = 583, 29115 = 586, 29415 = 589, 2AB15 = 611, 2B815 = 623, 2BB15 = 626, 2BE15 = 629, 2C415 = 634, 30A15 = 685, 30E15 = 689, 32C15 = 717, 35515 = 755, 36215 = 767, 38815 = 803, 38C15 = 807, 39515 = 815, 39715 = 817, 3B115 = 841, 3BB15 = 851, 3CA15 = 865, 3EA15 = 895, 40D15 = 913, 41215 = 917, 41615 = 921, 41715 = 922, 41815 = 923, 42915 = 939, 42D15 = 943, 43D15 = 958, 43E15 = 959, 44115 = 961, 44515 = 965, 44E15 = 974, 45715 = 982, 45A15 = 985, 46515 = 995, 46815 = 998

16

1615 = 21, 1715 = 22, 1B15 = 26, 2415 = 34, 2515 = 35, 2815 = 38, 3615 = 51, 3C15 = 57, 4215 = 62, 4E15 = 74, 5215 = 77, 5A15 = 85, 5C15 = 87, 6115 = 91, 6315 = 93, 7115 = 106, 7D15 = 118, 7E15 = 119, 8215 = 122, 8915 = 129, 8D15 = 133, 8E15 = 134, 9815 = 143, 9A15 = 145, A515 = 155, A915 = 159, B115 = 166, BD15 = 178, C315 = 183, C515 = 185, D715 = 202, D815 = 203, DB15 = 206, E415 = 214, E715 = 217, E815 = 218, 10C15 = 237, 11715 = 247, 11915 = 249, 11D15 = 253, 11E15 = 254, 14215 = 287, 14415 = 289, 14615 = 291, 14D15 = 298, 15215 = 302, 15915 = 309, 15E15 = 314, 16615 = 321, 16815 = 323, 16B15 = 326, 16E15 = 329, 17415 = 334, 17B15 = 341, 18D15 = 358, 19215 = 362, 19515 = 365, 19B15 = 371, 1A615 = 381, 1A715 = 382, 1B315 = 393, 1B815 = 398, 1BD15 = 403, 1C815 = 413, 1CC15 = 417, 1EA15 = 445, 1EC15 = 447, 21415 = 469, 21815 = 473, 21D15 = 478, 22515 = 485, 23615 = 501, 23715 = 502, 24115 = 511, 25115 = 526, 25A15 = 535, 26315 = 543, 26B15 = 551, 26D15 = 553, 26E15 = 554, 27415 = 559, 27B15 = 566, 28915 = 579, 28D15 = 583, 29115 = 586, 29415 = 589, 2AB15 = 611, 2B815 = 623, 2BB15 = 626, 2BE15 = 629, 2C415 = 634, 30A15 = 685, 30E15 = 689, 32C15 = 717, 35515 = 755, 36215 = 767, 38815 = 803, 38C15 = 807, 39515 = 815, 39715 = 817, 3B115 = 841, 3BB15 = 851, 3CA15 = 865, 3EA15 = 895, 40D15 = 913, 41215 = 917, 41615 = 921, 41715 = 922, 41815 = 923, 42915 = 939, 42D15 = 943, 43D15 = 958, 43E15 = 959, 44115 = 961, 44515 = 965, 44E15 = 974, 45715 = 982, 45A15 = 985, 46515 = 995, 46815 = 998

17

1417 = 21, 1517 = 22, 2517 = 39, 2C17 = 46, 3717 = 58, 4117 = 69, 4617 = 74, 5117 = 86, 5217 = 87, 5817 = 93, 5917 = 94, 6417 = 106, 6917 = 111, 6G17 = 118, 7317 = 122, 7A17 = 129, 7F17 = 134, 8517 = 141, 8917 = 145, 8A17 = 146, 9517 = 158, 9617 = 159, 9817 = 161, A717 = 177, A817 = 178, AF17 = 185, BE17 = 201, C217 = 206, CF17 = 219, EB17 = 249, F717 = 262, FA17 = 265, FC17 = 267, G617 = 278, 10217 = 291, 10617 = 295, 10917 = 298, 10D17 = 302, 11F17 = 321, 12017 = 323, 12417 = 327, 12617 = 329, 12B17 = 334, 12C17 = 335, 12G17 = 339, 13F17 = 355, 14517 = 362, 14E17 = 371, 15C17 = 386, 16217 = 393, 16717 = 398, 16G17 = 407, 17517 = 413, 17917 = 417, 17E17 = 422, 19C17 = 454, 19G17 = 458, 1A717 = 466, 1AC17 = 471, 1B217 = 478, 1B517 = 481, 1C017 = 493, 1C817 = 501, 1D717 = 517, 1D917 = 519, 1DG17 = 526, 1E217 = 529, 1EB17 = 538, 1EF17 = 542, 1EG17 = 543, 1F717 = 551, 1G517 = 566, 20117 = 579, 20317 = 581, 22B17 = 623, 24G17 = 662, 25417 = 667, 25617 = 669, 25G17 = 679, 26117 = 681, 26717 = 687, 26917 = 689, 26F17 = 695, 27017 = 697, 27917 = 706, 28417 = 718, 29017 = 731, 2A717 = 755, 2AA17 = 758, 2B117 = 766, 2B617 = 771, 2BD17 = 778, 2C317 = 785, 2C717 = 789, 2C917 = 791, 2CB17 = 793, 2D417 = 803, 2DE17 = 813, 2DG17 = 815, 2E117 = 817, 2F817 = 841, 2F917 = 842, 2FA17 = 843, 2FG17 = 849, 2GC17 = 862, 2GF17 = 865, 30217 = 869, 30417 = 871, 31517 = 889, 31B17 = 895, 32C17 = 913, 32G17 = 917, 33G17 = 934, 34417 = 939, 34E17 = 949, 35617 = 958, 35D17 = 965, 36417 = 973, 36A17 = 979, 36D17 = 982, 37917 = 995

18

1318 = 21, 1818 = 26, 1G18 = 34, 3118 = 55, 3B18 = 65, 4518 = 77, 4F18 = 87, 5418 = 94, 7G18 = 142, 8118 = 145, 8B18 = 155, 8F18 = 159, 8H18 = 161, AE18 = 194, B318 = 201, B818 = 206, BG18 = 214, EA18 = 262, F418 = 274, F818 = 278, FH18 = 287, G118 = 289, G718 = 295, GB18 = 299, H818 = 314, HF18 = 321, 10218 = 326, 10318 = 327, 10A18 = 334, 10H18 = 341, 11418 = 346, 12218 = 362, 12B18 = 371, 12H18 = 377, 13318 = 381, 13418 = 382, 13D18 = 391, 13F18 = 393, 14218 = 398, 15D18 = 427, 16D18 = 445, 16E18 = 446, 17318 = 453, 17G18 = 466, 18518 = 473, 18A18 = 478, 18E18 = 482, 19318 = 489, 1A718 = 511, 1AA18 = 514, 1AD18 = 517, 1AF18 = 519, 1B518 = 527, 1BB18 = 533, 1BD18 = 535, 1BG18 = 538, 1C218 = 542, 1C318 = 543, 1C518 = 545, 1CB18 = 551, 1CD18 = 553, 1D818 = 566, 1DF18 = 573, 1EA18 = 586, 1F318 = 597, 1H418 = 634, 1H518 = 635, 20118 = 649, 20E18 = 662, 22118 = 685, 22518 = 689, 22B18 = 695, 22E18 = 698, 24118 = 721, 24318 = 723, 24H18 = 737, 28A18 = 802, 28F18 = 807, 2A318 = 831, 2AF18 = 843, 2C118 = 865, 2C518 = 869, 2CE18 = 878, 2CF18 = 879, 2E518 = 905, 2G318 = 939, 2G718 = 943, 2GD18 = 949, 30118 = 973, 30718 = 979, 31518 = 995

19

1219 = 21, 1319 = 22, 1619 = 25, 1719 = 26, 1E19 = 33, 1G19 = 35, 2119 = 39, 2D19 = 51, 3119 = 58, 3819 = 65, 3H19 = 74, 4619 = 82, 4A19 = 86, 4B19 = 87, 4F19 = 91, 4H19 = 93, 4I19 = 94, 5B19 = 106, 5G19 = 111, 6119 = 115, 6419 = 118, 6819 = 122, 6919 = 123, 6F19 = 129, 7119 = 134, 7819 = 141, 7919 = 142, 7C19 = 145, 7D19 = 146, 8319 = 155, 8619 = 158, 8719 = 159, 8E19 = 166, 9619 = 177, 9719 = 178, 9C19 = 183, A419 = 194, AB19 = 201, AF19 = 205, AG19 = 206, B419 = 213, B519 = 214, BA19 = 219, BH19 = 226, C719 = 235, C919 = 237, D219 = 249, D719 = 254, DF19 = 262, DI19 = 265, E119 = 267, E819 = 274, F419 = 289, F619 = 291, FA19 = 295, FD19 = 298, FG19 = 301, G119 = 305, G519 = 309, GA19 = 314, GF19 = 319, GH19 = 321, H319 = 326, H419 = 327, HB19 = 334, HG19 = 339, I419 = 346, ID19 = 355, 10A19 = 371, 10G19 = 377, 11619 = 386, 11B19 = 391, 11D19 = 393, 11F19 = 395, 11I19 = 398, 12E19 = 413, 12G19 = 415, 12I19 = 417, 13419 = 422, 14019 = 437, 14819 = 445, 14919 = 446, 14A19 = 447, 14E19 = 451, 14G19 = 453, 15219 = 458, 15H19 = 473, 16319 = 478, 16719 = 482, 16E19 = 489, 16I19 = 493, 17719 = 501, 17819 = 502, 17B19 = 505, 18619 = 519, 18D19 = 526, 18E19 = 527, 19319 = 535, 19519 = 537, 19B19 = 543, 1A219 = 553, 1AB19 = 562, 1AE19 = 565, 1AF19 = 566, 1B319 = 573, 1B919 = 579, 1BB19 = 581, 1C219 = 591, 1C819 = 597, 1DF19 = 623, 1DI19 = 626, 1E219 = 629, 1E619 = 633, 1E819 = 635, 1F319 = 649, 1G219 = 667, 1G619 = 671, 1G919 = 674, 1GE19 = 679, 1GG19 = 681, 1HB19 = 695, 1HD19 = 697, 1HE19 = 698, 1HF19 = 699, 1IA19 = 713, 1IF19 = 718, 21419 = 745, 21C19 = 753, 21H19 = 758, 22619 = 766, 22719 = 767, 23A19 = 789, 24419 = 802, 24519 = 803, 24919 = 807, 24F19 = 813, 25119 = 818, 25I19 = 835, 26519 = 841, 26719 = 843, 27B19 = 866, 27G19 = 871, 28519 = 879, 28C19 = 886, 2A119 = 913, 2AA19 = 922, 2AB19 = 923, 2B319 = 934, 2B819 = 939, 2C119 = 951, 2C819 = 958, 2CF19 = 965, 2DA19 = 979, 2E119 = 989, 2E519 = 993

20

1620 = 26, 1F20 = 35, 1I20 = 38, 1J20 = 39, 2620 = 46, 2F20 = 55, 2I20 = 58, 3920 = 69, 5F20 = 115, 5I20 = 118, 6120 = 121, 6220 = 122, 9320 = 183, 9E20 = 194, E920 = 289, EF20 = 295, EJ20 = 299, F120 = 301, F220 = 302, F520 = 305, FE20 = 314, FJ20 = 319, HI20 = 358, I120 = 361, I220 = 362, I520 = 365, IH20 = 377, J120 = 381, JE20 = 394, JF20 = 395, 10D20 = 413, 10F20 = 415, 10H20 = 417, 11H20 = 437, 12520 = 445, 12720 = 447, 12D20 = 453, 12I20 = 458, 13620 = 466, 13920 = 469, 13B20 = 471, 13I20 = 478, 14H20 = 497, 15220 = 502, 15520 = 505, 15B20 = 511, 15H20 = 517, 16720 = 527, 16920 = 529, 16D20 = 533, 17B20 = 551, 18220 = 562, 18620 = 566, 18D20 = 573, 19620 = 586, 19920 = 589, 1AB20 = 611, 1C920 = 649, 1CF20 = 655, 1DB20 = 671, 1DJ20 = 679, 1EF20 = 695, 1EH20 = 697, 1F320 = 703, 1F620 = 706, 1F720 = 707, 1FI20 = 718, 1GE20 = 734, 1H920 = 749, 1HD20 = 753, 1HF20 = 755, 1I320 = 763, 1I620 = 766, 1I720 = 767, 1IJ20 = 779, 1J920 = 789, 1JB20 = 791, 1JJ20 = 799, 20320 = 803, 20F20 = 815, 21F20 = 835, 22B20 = 851, 23520 = 865, 23620 = 866, 23920 = 869, 23I20 = 878, 24F20 = 895, 25120 = 901, 25520 = 905, 25E20 = 914, 26320 = 923, 26E20 = 934, 27920 = 949, 27I20 = 958, 28120 = 961, 28J20 = 979, 29520 = 985, 29I20 = 998

 

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