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Semiprimi troncabili

Rappresentazione dei numeri 

Nel 2007 Shyam Sunder Gupta chiamò “semiprimi troncabili” i semiprimi che non contengono zeri e che restano semiprimi se ad essi vengono progressivamente tolte cifre, fino a restare con un semiprimo di una sola cifra.

 

Dato che le cifre possono essere tolte sia da destra che da sinistra, esistono due categorie di semiprimi troncabili: i semiprimi troncabili a destra e quelli troncabili a sinistra.

Per esempio, 933593 è un semiprimo troncabile da destra, perché 93359, 9335, 933, 93 e 9 sono semiprimi.

Per esempio, 997939 è un semiprimo troncabile da sinistra, perché 97939, 7939, 939, 39 e 9 sono semiprimi.

 

La definizione ricalca quella dei primi troncabili.

La definizione originale prevedeva l’esclusione della cifra zero; con questo vincolo Gupta determinò che vi sono in tutto 56076 semiprimi troncabili a destra, il massimo dei quali è 95861957783594714393831931415189937897; qualsiasi cifra aggiunta a destra produce un numero che non è semiprimo.

 

Il concetto di semiprimi troncabili si può generalizzare ad altre basi.

Sperimentalmente sembra che non ammettendo l’uso dello zero i semiprimi siano in numero finito, fissata la base, con entrambe le definizioni.

 

Ammettendo l’uso dello zero i semiprimi troncabili a destra aumentano, ma sembrano essere in numero finito in tutte le basi, mentre non è assolutamente chiaro se quelli troncabili a sinistra possano essere infiniti in qualche base.

 

La tabella seguente mostra i semiprimi troncabili a destra minori di 109 nelle basi fino a 20, includendo lo zero tra le cifre ammesse.

Base

Semiprimi

2

-

3

-

4

-

5

45 = 4, 415 = 21, 425 = 22, 4115 = 106, 4215 = 111, 41135 = 533, 42145 = 559

6

46 = 4, 416 = 25, 426 = 26, 4156 = 155, 4226 = 158, 4236 = 159, 4256 = 161, 41536 = 933, 41546 = 934, 42216 = 949, 42236 = 951, 42316 = 955, 42346 = 958, 42356 = 959

7

47 = 4, 67 = 6, 457 = 33, 467 = 34, 647 = 46, 4547 = 235, 4567 = 237, 6417 = 323, 6447 = 326, 6457 = 327

8

48 = 4, 68 = 6, 418 = 33, 428 = 34, 438 = 35, 468 = 38, 478 = 39, 618 = 49, 638 = 51, 678 = 55, 4118 = 265, 4138 = 267, 4228 = 274, 4268 = 278, 4378 = 287, 4618 = 305, 4658 = 309, 4728 = 314, 4778 = 319, 6118 = 393, 6128 = 394, 6138 = 395, 6168 = 398, 6338 = 411, 6358 = 413, 6378 = 415, 6758 = 445, 6768 = 446, 6778 = 447

9

49 = 4, 69 = 6, 429 = 38, 439 = 39, 619 = 55, 639 = 57, 649 = 58, 689 = 62, 4249 = 346, 4349 = 355, 4379 = 358, 6129 = 497, 6169 = 501, 6179 = 502, 6319 = 514, 6329 = 515, 6349 = 517, 6369 = 519, 6449 = 526, 6459 = 527, 6479 = 529, 6819 = 559, 6849 = 562, 6879 = 565, 6889 = 566

10

4, 6, 9, 46, 49, 62, 65, 69, 91, 93, 94, 95, 466, 469, 493, 497, 622, 623, 626, 629, 655, 694, 695, 697, 698, 699, 913, 914, 917, 933, 934, 939, 943, 949, 951, 955, 958, 959

11

411 = 4, 611 = 6, 911 = 9, A11 = 10, 4211 = 46, 4511 = 49, 4711 = 51, 6311 = 69, 6811 = 74, 9711 = 106, A111 = 111, A511 = 115, A811 = 118, A911 = 119, 42511 = 511, 42811 = 514, 42911 = 515, 45311 = 542, 45411 = 543, 45611 = 545, 47111 = 562, 47411 = 565, 47511 = 566, 63411 = 763, 63711 = 766, 63811 = 767, 68111 = 815, 68311 = 817, 68411 = 818

12

412 = 4, 612 = 6, 912 = 9, A12 = 10, 4112 = 49, 4312 = 51, 4712 = 55, 4912 = 57, 4A12 = 58, 6212 = 74, 6512 = 77, 6A12 = 82, 9312 = 111, 9712 = 115, 9A12 = 118, 9B12 = 119, A112 = 121, A212 = 122, A312 = 123, A912 = 129, 41112 = 589, 41312 = 591, 41912 = 597, 43212 = 614, 43A12 = 622, 43B12 = 623, 47212 = 662, 47712 = 667, 47912 = 669, 47B12 = 671, 49112 = 685, 49312 = 687, 49512 = 689, 49A12 = 694, 49B12 = 695, 4A112 = 697, 4A212 = 698, 4A312 = 699, 4A712 = 703, 4AA12 = 706, 4AB12 = 707, 62112 = 889, 62512 = 893, 62712 = 895, 62A12 = 898, 62B12 = 899, 65212 = 926, 65912 = 933, 65A12 = 934, 6A112 = 985, 6A512 = 989, 6A912 = 993, 6AB12 = 995

13

413 = 4, 613 = 6, 913 = 9, A13 = 10, 4313 = 55, 4513 = 57, 4613 = 58, 4A13 = 62, 6413 = 82, 6713 = 85, 6813 = 86, 6913 = 87, 9113 = 118, 9213 = 119, 9413 = 121, 9513 = 122, 9613 = 123, 9C13 = 129, A313 = 133, A413 = 134, AB13 = 141, AC13 = 142, 43213 = 717, 43313 = 718, 43613 = 721, 43813 = 723, 45413 = 745, 45513 = 746, 45813 = 749, 45C13 = 753, 46113 = 755, 46413 = 758, 46913 = 763, 46C13 = 766, 4A113 = 807, 4A713 = 813, 4A913 = 815, 4AB13 = 817, 4AC13 = 818

14

414 = 4, 614 = 6, 914 = 9, A14 = 10, 4114 = 57, 4214 = 58, 4614 = 62, 4914 = 65, 4D14 = 69, 6114 = 85, 6214 = 86, 6314 = 87, 6714 = 91, 6914 = 93, 6A14 = 94, 6B14 = 95, 9314 = 129, 9714 = 133, 9814 = 134, A114 = 141, A214 = 142, A314 = 143, A514 = 145, A614 = 146, 41114 = 799, 41414 = 802, 41514 = 803, 41914 = 807, 42114 = 813, 42314 = 815, 42514 = 817, 42614 = 818, 46114 = 869, 46314 = 871, 46A14 = 878, 46B14 = 879, 49314 = 913, 49414 = 914, 49714 = 917, 49B14 = 921, 49C14 = 922, 49D14 = 923, 4D714 = 973, 4D814 = 974, 4DD14 = 979

15

415 = 4, 615 = 6, 915 = 9, A15 = 10, E15 = 14, 4215 = 62, 4515 = 65, 4915 = 69, 4E15 = 74, 6115 = 91, 6315 = 93, 6415 = 94, 6515 = 95, 9615 = 141, 9715 = 142, 9815 = 143, 9A15 = 145, 9B15 = 146, A515 = 155, A815 = 158, A915 = 159, AB15 = 161, E315 = 213, E415 = 214, E515 = 215, E715 = 217, E815 = 218, E915 = 219, EB15 = 221, 42315 = 933, 42415 = 934, 42915 = 939, 42D15 = 943, 45415 = 979, 45715 = 982, 45A15 = 985, 45E15 = 989

16

416 = 4, 616 = 6, 916 = 9, A16 = 10, E16 = 14, F16 = 15, 4116 = 65, 4516 = 69, 4A16 = 74, 4D16 = 77, 6A16 = 106, 6F16 = 111, 9116 = 145, 9216 = 146, 9B16 = 155, 9E16 = 158, 9F16 = 159, A116 = 161, A616 = 166, A916 = 169, E216 = 226, EB16 = 235, ED16 = 237, F716 = 247, F916 = 249, FD16 = 253, FE16 = 254

17

417 = 4, 617 = 6, 917 = 9, A17 = 10, E17 = 14, F17 = 15, 4117 = 69, 4617 = 74, 4917 = 77, 4E17 = 82, 6417 = 106, 6917 = 111, 6D17 = 115, 6G17 = 118, 9217 = 155, 9517 = 158, 9617 = 159, 9817 = 161, 9D17 = 166, 9G17 = 169, A717 = 177, A817 = 178, AD17 = 183, AF17 = 185, E917 = 247, EB17 = 249, EF17 = 253, EG17 = 254, F417 = 259, F717 = 262, FA17 = 265, FC17 = 267

18

418 = 4, 618 = 6, 918 = 9, A18 = 10, E18 = 14, F18 = 15, 4218 = 74, 4518 = 77, 4A18 = 82, 4D18 = 85, 4E18 = 86, 4F18 = 87, 6318 = 111, 6718 = 115, 6A18 = 118, 6B18 = 119, 6D18 = 121, 6E18 = 122, 6F18 = 123, 9418 = 166, 9718 = 169, 9F18 = 177, 9G18 = 178, A318 = 183, A518 = 185, A718 = 187, AE18 = 194, E118 = 253, E218 = 254, E718 = 259, EA18 = 262, ED18 = 265, EF18 = 267, F418 = 274, F818 = 278, FH18 = 287

19

419 = 4, 619 = 6, 919 = 9, A19 = 10, E19 = 14, F19 = 15, 4119 = 77, 4619 = 82, 4919 = 85, 4A19 = 86, 4B19 = 87, 4F19 = 91, 4H19 = 93, 4I19 = 94, 6119 = 115, 6419 = 118, 6519 = 119, 6719 = 121, 6819 = 122, 6919 = 123, 6F19 = 129, 9619 = 177, 9719 = 178, 9C19 = 183, 9E19 = 185, 9G19 = 187, A419 = 194, AB19 = 201, AC19 = 202, AD19 = 203, AF19 = 205, AG19 = 206, E119 = 267, E819 = 274, EC19 = 278, F219 = 287, F419 = 289, F619 = 291, FA19 = 295, FD19 = 298, FE19 = 299, FG19 = 301, FH19 = 302, FI19 = 303

20

420 = 4, 620 = 6, 920 = 9, A20 = 10, E20 = 14, F20 = 15, 4220 = 82, 4520 = 85, 4620 = 86, 4720 = 87, 4B20 = 91, 4D20 = 93, 4E20 = 94, 4F20 = 95, 6120 = 121, 6220 = 122, 6320 = 123, 6920 = 129, 6D20 = 133, 6E20 = 134, 9320 = 183, 9520 = 185, 9720 = 187, 9E20 = 194, A120 = 201, A220 = 202, A320 = 203, A520 = 205, A620 = 206, A920 = 209, AD20 = 213, AE20 = 214, AF20 = 215, AH20 = 217, AI20 = 218, AJ20 = 219, E720 = 287, E920 = 289, EB20 = 291, EF20 = 295, EI20 = 298, EJ20 = 299, F120 = 301, F220 = 302, F320 = 303, F520 = 305, F920 = 309, FE20 = 314, FJ20 = 319

 

La tabella seguente mostra i semiprimi troncabili a sinistra minori di 109 nelle basi fino a 20, includendo lo zero tra le cifre ammesse.

Base

Semiprimi

2

-

3

-

4

-

5

45 = 4, 145 = 9, 245 = 14, 1145 = 34, 1245 = 39, 10045 = 129, 10145 = 134, 11145 = 159, 20045 = 254, 20145 = 259, 21245 = 289, 40245 = 514, 100045 = 629, 100145 = 634, 120045 = 879, 121245 = 914

6

46 = 4, 146 = 10, 346 = 22, 546 = 34, 1146 = 46, 1346 = 58, 2146 = 82, 2346 = 94, 2546 = 106, 3146 = 118, 3546 = 142, 4346 = 166, 4546 = 178, 5346 = 202, 5546 = 214, 10146 = 226, 11146 = 262, 11346 = 274, 12146 = 298, 13146 = 334, 13546 = 358, 14346 = 382, 14546 = 394, 20346 = 454, 20546 = 466, 21146 = 478, 22146 = 514, 22346 = 526, 22546 = 538, 25346 = 634, 31146 = 694, 31346 = 706, 33146 = 766, 35546 = 862, 40346 = 886, 40546 = 898, 41346 = 922, 42346 = 958, 43146 = 982

7

47 = 4, 67 = 6, 347 = 25, 467 = 34, 547 = 39, 647 = 46, 1067 = 55, 1347 = 74, 1647 = 95, 2347 = 123, 4067 = 202, 4347 = 221, 4547 = 235, 5047 = 249, 5647 = 291, 6047 = 298, 6347 = 319, 10467 = 377, 10547 = 382, 11067 = 398, 11347 = 417, 12347 = 466, 14067 = 545, 15647 = 634, 16347 = 662, 21647 = 781, 24547 = 921

8

48 = 4, 68 = 6, 168 = 14, 268 = 22, 468 = 38, 568 = 46, 768 = 62, 1268 = 86, 2068 = 134, 2168 = 142, 2468 = 166, 3168 = 206, 3268 = 214, 3768 = 254, 4068 = 262, 4268 = 278, 4568 = 302, 5068 = 326, 5168 = 334, 5468 = 358, 5768 = 382, 6168 = 398, 6468 = 422, 6768 = 446, 7068 = 454, 10168 = 526, 13168 = 718, 13768 = 766, 15068 = 838, 16468 = 934, 16768 = 958

9

49 = 4, 69 = 6, 169 = 15, 249 = 22, 369 = 33, 549 = 49, 569 = 51, 649 = 58, 769 = 69, 1049 = 85, 1069 = 87, 2049 = 166, 2169 = 177, 2569 = 213, 3049 = 247, 3069 = 249, 3249 = 265, 3649 = 301, 4169 = 339, 4249 = 346, 4649 = 382, 4769 = 393, 5069 = 411, 5249 = 427, 5549 = 454, 6169 = 501, 6369 = 519, 6549 = 535, 6569 = 537, 7069 = 573, 7249 = 589, 8369 = 681, 8549 = 697, 8569 = 699, 8649 = 706, 8769 = 717, 10549 = 778, 12049 = 895

10

4, 6, 9, 14, 26, 34, 39, 46, 49, 69, 74, 86, 94, 106, 134, 146, 169, 194, 206, 209, 214, 226, 249, 274, 309, 314, 326, 334, 339, 346, 386, 394, 446, 469, 514, 526, 586, 614, 626, 634, 649, 669, 674, 694, 706, 734, 746, 749, 794, 849, 869, 886, 914, 926, 934, 939, 949, 974

11

411 = 4, 611 = 6, 911 = 9, A11 = 10, 1411 = 15, 1A11 = 21, 2411 = 26, 3611 = 39, 5A11 = 65, 7911 = 86, 7A11 = 87, 8611 = 94, A911 = 119, 11A11 = 142, 18611 = 215, 27A11 = 329, 2A911 = 361, 3A911 = 482, 40911 = 493, 41A11 = 505, 50611 = 611, 50911 = 614, 51A11 = 626, 58611 = 699, 65A11 = 791, 67A11 = 813, 70411 = 851, 71411 = 862, 73611 = 886, 77911 = 933, 77A11 = 934, 80611 = 974, 81A11 = 989

12

412 = 4, 612 = 6, 912 = 9, A12 = 10, 1912 = 21, 1A12 = 22, 2912 = 33, 2A12 = 34, 3A12 = 46, 4912 = 57, 4A12 = 58, 5912 = 69, 6A12 = 82, 7912 = 93, 7A12 = 94, 8A12 = 106, 9A12 = 118, A912 = 129, B912 = 141, BA12 = 142, 11A12 = 166, 12912 = 177, 12A12 = 178, 14912 = 201, 14A12 = 202, 15912 = 213, 16A12 = 226, 17912 = 237, 19A12 = 262, 20A12 = 298, 21912 = 309, 22912 = 321, 23A12 = 334, 24A12 = 346, 27912 = 381, 27A12 = 382, 28A12 = 394, 2A912 = 417, 31912 = 453, 31A12 = 454, 32A12 = 466, 33A12 = 478, 34912 = 489, 35912 = 501, 36A12 = 514, 37A12 = 526, 38A12 = 538, 3B912 = 573, 40A12 = 586, 41912 = 597, 43A12 = 622, 44912 = 633, 44A12 = 634, 47912 = 669, 49A12 = 694, 4B912 = 717, 4BA12 = 718, 52912 = 753, 53A12 = 766, 54A12 = 778, 55912 = 789, 56A12 = 802, 57912 = 813, 59A12 = 838, 5A912 = 849, 5BA12 = 862, 61A12 = 886, 62A12 = 898, 64912 = 921, 64A12 = 922, 65912 = 933, 67A12 = 958, 69A12 = 982, 6A912 = 993

13

413 = 4, 613 = 6, 913 = 9, A13 = 10, 1913 = 22, 2913 = 35, 3A13 = 49, 4613 = 58, 4A13 = 62, 5413 = 69, 5913 = 74, 6413 = 82, 6913 = 87, 7413 = 95, 9413 = 121, 9613 = 123, A413 = 134, CA13 = 166, 10913 = 178, 13A13 = 218, 1A413 = 303, 1CA13 = 335, 25413 = 407, 30413 = 511, 30A13 = 517, 31913 = 529, 32913 = 542, 34613 = 565, 35913 = 581, 36413 = 589, 40913 = 685, 41913 = 698, 44613 = 734, 45413 = 745, 46413 = 758, 46913 = 763, 47413 = 771, 49613 = 799, 4CA13 = 842, 50413 = 849, 50613 = 851, 55413 = 914, 5A413 = 979

14

414 = 4, 614 = 6, 914 = 9, A14 = 10, 2614 = 34, 2A14 = 38, 3414 = 46, 3914 = 51, 4614 = 62, 4914 = 65, 5414 = 74, 6914 = 93, 6A14 = 94, 8614 = 118, 8914 = 121, 8A14 = 122, A614 = 146, B414 = 158, C914 = 177, CA14 = 178, 10614 = 202, 10914 = 205, 10A14 = 206, 13914 = 247, 16914 = 289, 18614 = 314, 20614 = 398, 24614 = 454, 25414 = 466, 26914 = 485, 28A14 = 514, 2A614 = 538, 30914 = 597, 32614 = 622, 32A14 = 626, 33414 = 634, 35414 = 662, 36914 = 681, 38614 = 706, 3A614 = 734, 3B414 = 746, 3CA14 = 766, 40914 = 793, 40A14 = 794, 42614 = 818, 43914 = 835, 44914 = 849, 46A14 = 878, 48914 = 905, 4C914 = 961, 50914 = 989

15

415 = 4, 615 = 6, 915 = 9, A15 = 10, E15 = 14, 1615 = 21, 1A15 = 25, 2415 = 34, 2915 = 39, 3415 = 49, 3615 = 51, 3A15 = 55, 4915 = 69, 4E15 = 74, 5A15 = 85, 6415 = 94, 7615 = 111, 7A15 = 115, 7E15 = 119, 8915 = 129, 8E15 = 134, 9615 = 141, 9A15 = 145, A915 = 159, B415 = 169, CE15 = 194, D615 = 201, DA15 = 205, DE15 = 209, E415 = 214, E915 = 219, 10A15 = 235, 12415 = 259, 13415 = 274, 14E15 = 299, 16415 = 319, 1B415 = 394, 20415 = 454, 21615 = 471, 22915 = 489, 23615 = 501, 23A15 = 505, 24915 = 519, 25A15 = 535, 27A15 = 565, 28915 = 579, 29615 = 591, 2DA15 = 655, 2E915 = 669, 30415 = 679, 30615 = 681, 30A15 = 685, 30E15 = 689, 34E15 = 749, 37E15 = 794, 3CE15 = 869, 3E415 = 889, 40E15 = 914, 41615 = 921, 42415 = 934, 42915 = 939, 43415 = 949, 43615 = 951, 43A15 = 955, 44E15 = 974, 45A15 = 985

16

416 = 4, 616 = 6, 916 = 9, A16 = 10, E16 = 14, F16 = 15, 1616 = 22, 1916 = 25, 1A16 = 26, 2616 = 38, 2E16 = 46, 3916 = 57, 3A16 = 58, 3E16 = 62, 4A16 = 74, 5616 = 86, 5E16 = 94, 5F16 = 95, 6A16 = 106, 6F16 = 111, 7616 = 118, 7916 = 121, 7A16 = 122, 8616 = 134, 8E16 = 142, 8F16 = 143, 9E16 = 158, 9F16 = 159, A616 = 166, A916 = 169, B916 = 185, C916 = 201, CA16 = 202, CE16 = 206, D616 = 214, D916 = 217, DA16 = 218, F916 = 249, FE16 = 254, 10616 = 262, 10916 = 265, 11616 = 278, 12E16 = 302, 13A16 = 314, 16A16 = 362, 17916 = 377, 18E16 = 398, 19F16 = 415, 1A616 = 422, 1CA16 = 458, 1D916 = 473, 1F916 = 505, 20E16 = 526, 20F16 = 527, 21916 = 537, 21A16 = 538, 24A16 = 586, 26F16 = 623, 27916 = 633, 27A16 = 634, 28F16 = 655, 29F16 = 671, 2A916 = 681, 2B916 = 697, 2C916 = 713, 2CE16 = 718, 2FE16 = 766, 30A16 = 778, 31916 = 793, 31A16 = 794, 34A16 = 842, 35E16 = 862, 36F16 = 879, 37616 = 886, 37916 = 889, 39E16 = 926, 3A616 = 934, 3CE16 = 974, 3D616 = 982, 3D916 = 985

17

417 = 4, 617 = 6, 917 = 9, A17 = 10, E17 = 14, F17 = 15, 1417 = 21, 1917 = 26, 2417 = 38, 2F17 = 49, 3417 = 55, 3617 = 57, 3E17 = 65, 4617 = 74, 4917 = 77, 4E17 = 82, 5617 = 91, 5917 = 94, 5A17 = 95, 6417 = 106, 6917 = 111, 7417 = 123, 7A17 = 129, 7E17 = 133, 7F17 = 134, 8617 = 142, 8917 = 145, 8A17 = 146, 9617 = 159, AF17 = 185, BE17 = 201, BF17 = 202, C917 = 213, CA17 = 214, CE17 = 218, CF17 = 219, DE17 = 235, E917 = 247, EF17 = 253, F417 = 259, FA17 = 265, G617 = 278, GF17 = 287, 10617 = 295, 10917 = 298, 10A17 = 299, 10E17 = 303, 12417 = 327, 13617 = 346, 14E17 = 371, 16417 = 395, 17E17 = 422, 1C917 = 502, 1EF17 = 542, 1FA17 = 554, 23417 = 633, 23617 = 635, 24917 = 655, 25617 = 669, 26917 = 689, 27A17 = 707, 28917 = 723, 29617 = 737, 2AF17 = 763, 2BE17 = 779, 2C917 = 791, 2DE17 = 813, 2EF17 = 831, 2FA17 = 843, 2GF17 = 865, 30417 = 871, 31917 = 893, 32417 = 905, 33417 = 922, 34E17 = 949, 35617 = 958, 35917 = 961, 36417 = 973

18

418 = 4, 618 = 6, 918 = 9, A18 = 10, E18 = 14, F18 = 15, 1418 = 22, 1F18 = 33, 2A18 = 46, 2F18 = 51, 3418 = 58, 3F18 = 69, 4A18 = 82, 4E18 = 86, 4F18 = 87, 5418 = 94, 6A18 = 118, 6E18 = 122, 6F18 = 123, 7F18 = 141, 8E18 = 158, 8F18 = 159, 9418 = 166, 9F18 = 177, AE18 = 194, B418 = 202, BF18 = 213, CA18 = 226, DF18 = 249, EA18 = 262, EF18 = 267, F418 = 274, GA18 = 298, GE18 = 302, GF18 = 303, HF18 = 321, 10A18 = 334, 10F18 = 339, 11418 = 346, 13418 = 382, 13F18 = 393, 14F18 = 411, 16E18 = 446, 16F18 = 447, 18E18 = 482, 19F18 = 501, 1B418 = 526, 1BF18 = 537, 1DF18 = 573, 1EA18 = 586, 1EF18 = 591, 1GA18 = 622, 1GE18 = 626, 20E18 = 662, 21F18 = 681, 22A18 = 694, 22F18 = 699, 23418 = 706, 23F18 = 717, 24E18 = 734, 26A18 = 766, 26F18 = 771, 27F18 = 789, 28F18 = 807, 2AE18 = 842, 2F418 = 922, 2GF18 = 951, 30A18 = 982

19

419 = 4, 619 = 6, 919 = 9, A19 = 10, E19 = 14, F19 = 15, 1619 = 25, 1E19 = 33, 1F19 = 34, 4619 = 82, 4919 = 85, 4A19 = 86, 4F19 = 91, 6419 = 118, 6919 = 123, 6F19 = 129, 7919 = 142, 7A19 = 143, 8619 = 158, 8919 = 161, 8E19 = 166, 9619 = 177, 9E19 = 185, A419 = 194, AF19 = 205, B419 = 213, B619 = 215, B919 = 218, BA19 = 219, C919 = 237, D619 = 253, DF19 = 262, F419 = 289, F619 = 291, FA19 = 295, FE19 = 299, GA19 = 314, GF19 = 319, H419 = 327, H619 = 329, I419 = 346, 10419 = 365, 10A19 = 371, 11619 = 386, 11E19 = 394, 11F19 = 395, 14919 = 446, 14A19 = 447, 18619 = 519, 18E19 = 527, 19619 = 538, 1AF19 = 566, 1B919 = 579, 1D619 = 614, 1DF19 = 623, 1I419 = 707, 20919 = 731, 20F19 = 737, 21E19 = 755, 24919 = 807, 24F19 = 813, 26F19 = 851, 27A19 = 865, 29619 = 899, 2C919 = 959

20

420 = 4, 620 = 6, 920 = 9, A20 = 10, E20 = 14, F20 = 15, 1620 = 26, 1E20 = 34, 1F20 = 35, 2620 = 46, 2920 = 49, 2F20 = 55, 3920 = 69, 3E20 = 74, 4620 = 86, 4E20 = 94, 4F20 = 95, 5620 = 106, 5F20 = 115, 6920 = 129, 6E20 = 134, 7620 = 146, 7F20 = 155, 8620 = 166, 8920 = 169, 9E20 = 194, A620 = 206, A920 = 209, AE20 = 214, AF20 = 215, B620 = 226, BF20 = 235, C920 = 249, CE20 = 254, DE20 = 274, E920 = 289, EF20 = 295, F920 = 309, FE20 = 314, G620 = 326, G920 = 329, GE20 = 334, GF20 = 335, H620 = 346, HF20 = 355, J620 = 386, JE20 = 394, JF20 = 395, 10F20 = 415, 12620 = 446, 13920 = 469, 15F20 = 515, 16920 = 529, 18620 = 566, 1AE20 = 614, 1B620 = 626, 1BF20 = 635, 1C920 = 649, 1DE20 = 674, 1E920 = 689, 1EF20 = 695, 1GE20 = 734, 1H620 = 746, 1HF20 = 755, 1JE20 = 794, 20F20 = 815, 21F20 = 835, 22920 = 849, 23920 = 869, 24620 = 886, 24F20 = 895, 26E20 = 934, 27F20 = 955

 

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