def testRegularContinuedFractionToFraction73_29(self):
self.assertEqual(Fraction(73, 29), regularContinuedFractionToFraction([2, 1, 1, 14]))
candidates = [] for d in ds: x, y = 2, 1 if __name__ == '__main__': # print(sorted(generate())) # [(3.0, 2, 2), (5.0, 6, 2), (7.0, 3, 4), (7.0, 12, 2), (8.0, 7, 3), (9.0, 5, 4), (9.0, 20, 2), (10.0, 11, 3), (11.0, 30, 2), (13.0, 42, 2), (15.0, 14, 4), (15.0, 56, 2), (17.0, 8, 6), (17.0, 18, 4), (17.0, 32, 3), (17.0, 72, 2), (19.0, 10, 6), (19.0, 40, 3), (19.0, 90, 2), (21.0, 110, 2), (23.0, 33, 4), (23.0, 132, 2), (24.0, 23, 5), (25.0, 39, 4), (25.0, 156, 2), (26.0, 27, 5), (26.0, 75, 3), (27.0, 182, 2), (28.0, 87, 3), (29.0, 210, 2), (31.0, 15, 8), (31.0, 60, 4), (31.0, 240, 2), (33.0, 17, 8), (33.0, 68, 4), (33.0, 272, 2), (35.0, 34, 6), (35.0, 136, 3), (35.0, 306, 2), (37.0, 38, 6), (37.0, 152, 3), (37.0, 342, 2), (39.0, 95, 4), (39.0, 380, 2), (41.0, 105, 4), (41.0, 420, 2), (43.0, 462, 2), (44.0, 215, 3), (45.0, 506, 2), (46.0, 235, 3), (47.0, 138, 4), (47.0, 552, 2), (48.0, 47, 7), (49.0, 24, 10), (49.0, 96, 5), (49.0, 150, 4), (49.0, 600, 2), (50.0, 51, 7), (51.0, 26, 10), (51.0, 104, 5), (51.0, 650, 2), (53.0, 78, 6), (53.0, 312, 3), (53.0, 702, 2), (55.0, 21, 12), (55.0, 84, 6), (55.0, 189, 4), (55.0, 336, 3), (55.0, 756, 2), (57.0, 203, 4), (57.0, 812, 2), (59.0, 870, 2), (61.0, 930, 2), (62.0, 427, 3), (63.0, 62, 8), (63.0, 248, 4), (63.0, 992, 2), (64.0, 455, 3), (65.0, 66, 8), (65.0, 264, 4), (71.0, 35, 12), (71.0, 140, 6), (71.0, 315, 4), (71.0, 560, 3), (73.0, 37, 12), (73.0, 148, 6), (73.0, 333, 4), (73.0, 592, 3), (74.0, 219, 5), (76.0, 231, 5), (79.0, 390, 4), (80.0, 79, 9), (80.0, 711, 3), (81.0, 410, 4), (82.0, 83, 9), (82.0, 747, 3), (87.0, 473, 4), (89.0, 55, 12), (89.0, 220, 6), (89.0, 495, 4), (89.0, 880, 3), (91.0, 230, 6), (91.0, 920, 3), (95.0, 141, 8), (95.0, 564, 4), (97.0, 48, 14), (97.0, 147, 8), (97.0, 192, 7), (97.0, 588, 4), (99.0, 50, 14), (99.0, 98, 10), (99.0, 200, 7), (99.0, 392, 5), (101.0, 102, 10), (101.0, 408, 5), (103.0, 663, 4), (105.0, 689, 4), (107.0, 318, 6), (109.0, 330, 6), (111.0, 770, 4), (113.0, 798, 4), (119.0, 885, 4), (120.0, 119, 11), (121.0, 915, 4), (122.0, 123, 11), (124.0, 615, 5), (125.0, 434, 6), (126.0, 635, 5), (127.0, 28, 24), (127.0, 63, 16), (127.0, 112, 12), (127.0, 252, 8), (127.0, 448, 6), (129.0, 65, 16), (129.0, 260, 8), (143.0, 142, 12), (143.0, 568, 6), (145.0, 146, 12), (145.0, 584, 6), (146.0, 435, 7), (148.0, 447, 7), (149.0, 222, 10), (149.0, 888, 5), (151.0, 57, 20), (151.0, 228, 10), (151.0, 912, 5), (159.0, 395, 8), (161.0, 45, 24), (161.0, 80, 18), (161.0, 180, 12), (161.0, 320, 9), (161.0, 405, 8), (161.0, 720, 6), (163.0, 82, 18), (163.0, 328, 9), (163.0, 738, 6), (168.0, 167, 13), (170.0, 19, 39), (170.0, 171, 13), (179.0, 890, 6), (181.0, 910, 6), (191.0, 570, 8), (193.0, 582, 8), (195.0, 194, 14), (195.0, 776, 7), (197.0, 22, 42), (197.0, 88, 21), (197.0, 198, 14), (197.0, 792, 7), (199.0, 44, 30), (199.0, 99, 20), (199.0, 176, 15), (199.0, 275, 12), (199.0, 396, 10), (201.0, 101, 20), (201.0, 404, 10), (215.0, 321, 12), (217.0, 327, 12), (223.0, 777, 8), (224.0, 223, 15), (225.0, 791, 8), (226.0, 227, 15), (233.0, 377, 12), (241.0, 120, 22), (241.0, 480, 11), (242.0, 723, 9), (243.0, 122, 22), (243.0, 488, 11), (244.0, 135, 21), (244.0, 735, 9), (249.0, 155, 20), (249.0, 620, 10), (251.0, 70, 30), (251.0, 280, 15), (251.0, 630, 10), (255.0, 254, 16), (257.0, 258, 16), (271.0, 510, 12), (287.0, 143, 24), (287.0, 572, 12), (288.0, 287, 17), (289.0, 145, 24), (289.0, 580, 12), (290.0, 291, 17), (293.0, 438, 14), (295.0, 111, 28), (295.0, 444, 14), (299.0, 894, 10), (301.0, 906, 10), (305.0, 646, 12), (323.0, 322, 18), (325.0, 326, 18), (337.0, 168, 26), (337.0, 672, 13), (339.0, 170, 26), (339.0, 680, 13), (343.0, 817, 12), (351.0, 77, 40), (351.0, 308, 20), (359.0, 895, 12), (360.0, 359, 19), (361.0, 905, 12), (362.0, 363, 19), (377.0, 987, 12), (383.0, 573, 16), (385.0, 579, 16), (391.0, 195, 28), (391.0, 780, 14), (393.0, 197, 28), (393.0, 788, 14), (399.0, 398, 20), (401.0, 402, 20), (415.0, 299, 24), (424.0, 799, 15), (440.0, 439, 21), (442.0, 443, 21), (449.0, 126, 40), (449.0, 224, 30), (449.0, 350, 24), (449.0, 504, 20), (449.0, 896, 15), (451.0, 226, 30), (451.0, 904, 15), (483.0, 482, 22), (485.0, 54, 66), (485.0, 216, 33), (485.0, 486, 22), (485.0, 726, 18), (487.0, 183, 36), (487.0, 732, 18), (489.0, 305, 28), (511.0, 255, 32), (513.0, 257, 32), (528.0, 527, 23), (530.0, 59, 69), (530.0, 531, 23), (551.0, 759, 20), (575.0, 574, 24), (577.0, 128, 51), (577.0, 288, 34), (577.0, 578, 24), (579.0, 290, 34), (599.0, 897, 20), (601.0, 903, 20), (604.0, 335, 33), (624.0, 623, 25), (626.0, 627, 25), (638.0, 923, 21), (647.0, 323, 36), (649.0, 13, 180), (649.0, 52, 90), (649.0, 117, 60), (649.0, 208, 45), (649.0, 325, 36), (649.0, 468, 30), (675.0, 674, 26), (677.0, 678, 26), (685.0, 266, 42), (687.0, 602, 28), (701.0, 546, 30), (703.0, 858, 24), (721.0, 160, 57), (721.0, 360, 38), (723.0, 362, 38), (727.0, 273, 44), (728.0, 727, 27), (730.0, 731, 27), (737.0, 943, 24), (783.0, 782, 28), (785.0, 786, 28), (799.0, 399, 40), (801.0, 401, 40), (809.0, 505, 36), (840.0, 839, 29), (842.0, 843, 29), (881.0, 440, 42), (881.0, 990, 28), (883.0, 442, 42), (899.0, 898, 30), (901.0, 902, 30), (960.0, 959, 31), (962.0, 107, 93), (962.0, 963, 31), (967.0, 483, 44), (969.0, 485, 44), (1015.0, 381, 52), (1025.0, 114, 96), (1025.0, 456, 48), (1057.0, 528, 46), (1059.0, 530, 46), (1079.0, 165, 84), (1079.0, 660, 42), (1126.0, 115, 105), (1135.0, 994, 36), (1151.0, 92, 120), (1151.0, 207, 80), (1151.0, 368, 60), (1151.0, 575, 48), (1151.0, 828, 40), (1153.0, 577, 48), (1209.0, 755, 44), (1249.0, 624, 50), (1249.0, 975, 40), (1251.0, 626, 50), (1279.0, 710, 48), (1324.0, 159, 105), (1351.0, 108, 130), (1351.0, 300, 78), (1351.0, 432, 65), (1351.0, 507, 60), (1351.0, 675, 52), (1353.0, 677, 52), (1376.0, 935, 45), (1451.0, 174, 110), (1451.0, 696, 55), (1457.0, 728, 54), (1459.0, 730, 54), (1471.0, 690, 56), (1520.0, 31, 273), (1520.0, 279, 91), (1567.0, 348, 84), (1567.0, 783, 56), (1569.0, 785, 56), (1574.0, 91, 165), (1574.0, 819, 55), (1601.0, 178, 120), (1601.0, 712, 60), (1665.0, 221, 112), (1665.0, 884, 56), (1681.0, 840, 58), (1682.0, 187, 123), (1683.0, 842, 58), (1691.0, 470, 78), (1693.0, 658, 66), (1695.0, 371, 88), (1735.0, 651, 68), (1799.0, 899, 60), (1801.0, 901, 60), (1814.0, 555, 77), (1921.0, 960, 62), (1923.0, 962, 62), (1961.0, 545, 84), (2024.0, 175, 153), (2024.0, 567, 85), (2049.0, 41, 320), (2049.0, 164, 160), (2049.0, 656, 80), (2167.0, 813, 76), (2177.0, 153, 176), (2177.0, 612, 88), (2351.0, 282, 140), (2367.0, 518, 104), (2402.0, 267, 147), (2431.0, 285, 144), (2449.0, 544, 105), (2449.0, 850, 84), (2501.0, 278, 150), (2524.0, 303, 145), (2526.0, 707, 95), (2647.0, 993, 84), (2663.0, 407, 132), (2737.0, 608, 111), (3041.0, 855, 104), (3365.0, 374, 174), (3401.0, 357, 180), (3480.0, 71, 413), (3482.0, 43, 531), (3482.0, 387, 177), (3699.0, 74, 430), (3699.0, 296, 215), (3725.0, 874, 126), (3871.0, 860, 132), (3970.0, 539, 171), (3970.0, 891, 133), (4115.0, 714, 154), (4231.0, 940, 138), (4393.0, 793, 156), (4490.0, 499, 201), (4599.0, 437, 220), (4607.0, 188, 336), (4607.0, 423, 224), (4607.0, 752, 168), (4625.0, 514, 204), (4801.0, 294, 280), (4801.0, 384, 245), (4999.0, 204, 350), (4999.0, 816, 175), (5201.0, 234, 340), (5201.0, 416, 255), (5201.0, 936, 170), (5291.0, 270, 322), (5777.0, 642, 228), (5781.0, 590, 238), (5930.0, 659, 231), (6049.0, 525, 264), (6349.0, 762, 230), (6499.0, 130, 570), (6499.0, 520, 285), (6626.0, 795, 235), (6761.0, 345, 364), (7226.0, 803, 255), (7397.0, 822, 258), (7501.0, 186, 550), (7501.0, 744, 275), (7743.0, 158, 616), (7743.0, 632, 308), (7775.0, 69, 936), (7775.0, 276, 468), (7775.0, 621, 312), (7937.0, 558, 336), (8380.0, 551, 357), (8749.0, 378, 450), (8837.0, 982, 282), (9249.0, 185, 680), (9249.0, 740, 340), (9801.0, 29, 1820), (9801.0, 116, 910), (9801.0, 464, 455), (9801.0, 725, 364), (10093.0, 618, 406), (10405.0, 86, 1122), (10405.0, 344, 561), (10405.0, 774, 374), (10610.0, 131, 927), (10951.0, 876, 370), (11551.0, 924, 380), (11663.0, 238, 756), (11663.0, 952, 378), (11775.0, 161, 928), (11775.0, 644, 464), (12151.0, 93, 1260), (12151.0, 372, 630), (12151.0, 837, 420), (12799.0, 316, 720), (13447.0, 332, 738), (13449.0, 269, 820), (13719.0, 665, 532), (14849.0, 957, 480), (15124.0, 375, 781), (15871.0, 465, 736), (16855.0, 129, 1484), (16855.0, 516, 742), (17151.0, 938, 560), (17299.0, 346, 930), (17406.0, 515, 767), (18514.0, 595, 759), (18768.0, 383, 959), (18817.0, 768, 679), (19601.0, 162, 1540), (19601.0, 242, 1260), (19601.0, 450, 924), (19601.0, 648, 770), (19601.0, 800, 693), (19601.0, 882, 660), (19601.0, 968, 630), (19603.0, 58, 2574), (19603.0, 232, 1287), (19603.0, 522, 858), (21295.0, 154, 1716), (21295.0, 616, 858), (22899.0, 458, 1070), (24335.0, 46, 3588), (24335.0, 184, 1794), (24335.0, 414, 1196), (24335.0, 736, 897), (24648.0, 503, 1099), (27379.0, 810, 962), (27849.0, 557, 1180), (28799.0, 476, 1320), (29767.0, 492, 1342), (31212.0, 767, 1127), (33281.0, 585, 1376), (33639.0, 695, 1276), (33857.0, 418, 1656), (34595.0, 706, 1302), (34849.0, 697, 1320), (39689.0, 205, 2772), (39689.0, 820, 1386), (40899.0, 818, 1430), (42283.0, 638, 1674), (42435.0, 866, 1442), (46551.0, 209, 3220), (46551.0, 836, 1610), (48599.0, 297, 2820), (48599.0, 825, 1692), (48842.0, 67, 5967), (48842.0, 603, 1989), (49299.0, 986, 1570), (49730.0, 411, 2453), (51841.0, 245, 3312), (51841.0, 980, 1656), (52021.0, 190, 3774), (52021.0, 760, 1887), (56447.0, 668, 2184), (57499.0, 966, 1850), (57799.0, 76, 6630), (57799.0, 304, 3315), (57799.0, 475, 2652), (57799.0, 684, 2210), (58620.0, 671, 2263), (59535.0, 206, 4148), (59535.0, 824, 2074), (62423.0, 177, 4692), (62423.0, 708, 2346), (62425.0, 351, 3332), (66249.0, 53, 9100), (66249.0, 212, 4550), (66249.0, 848, 2275), (68122.0, 563, 2871), (70226.0, 243, 4505), (70226.0, 867, 2385), (73035.0, 494, 3286), (75263.0, 933, 2464), (75646.0, 715, 2829), (77617.0, 352, 4137), (79201.0, 704, 2985), (80801.0, 909, 2680), (85292.0, 247, 5427), (88751.0, 426, 4300), (88805.0, 246, 5662), (88805.0, 984, 2831), (95831.0, 385, 4884), (97970.0, 339, 5321), (100351.0, 892, 3360), (102151.0, 908, 3390), (106133.0, 942, 3458), (111555.0, 386, 5678), (113399.0, 413, 5580), (114243.0, 338, 6214), (118337.0, 978, 3784), (119071.0, 540, 5124), (120126.0, 875, 4061), (122695.0, 939, 4004), (126003.0, 218, 8534), (126003.0, 872, 4267), (137215.0, 469, 6336), (139128.0, 263, 8579), (143649.0, 425, 6968), (145925.0, 134, 12606), (145925.0, 536, 6303), (146411.0, 830, 5082), (156644.0, 815, 5487), (165337.0, 687, 6308), (165676.0, 591, 6815), (179777.0, 498, 8056), (193549.0, 474, 8890), (194399.0, 213, 13320), (194399.0, 852, 6660), (202501.0, 950, 6570), (213859.0, 370, 11118), (227528.0, 103, 22419), (227528.0, 927, 7473), (228151.0, 237, 14820), (228151.0, 948, 7410), (236926.0, 611, 9585), (237161.0, 705, 8932), (246401.0, 693, 9360), (258065.0, 354, 13716), (275561.0, 945, 8964), (284088.0, 983, 9061), (285769.0, 85, 30996), (285769.0, 340, 15498), (285769.0, 765, 10332), (306917.0, 118, 28254), (306917.0, 472, 14127), (332929.0, 985, 10608), (360449.0, 979, 11520), (392499.0, 314, 22150), (469224.0, 887, 15755), (470449.0, 864, 16005), (499850.0, 459, 23331), (500001.0, 89, 53000), (500001.0, 356, 26500), (515095.0, 201, 36332), (515095.0, 804, 18166), (522785.0, 561, 22072), (561799.0, 236, 36570), (561799.0, 944, 18285), (561835.0, 286, 33222), (605695.0, 609, 24544), (641602.0, 347, 34443), (665857.0, 512, 29427), (669337.0, 543, 28724), (669878.0, 403, 33369), (714024.0, 743, 26195), (842401.0, 832, 29205), (847225.0, 259, 52644), (848719.0, 310, 48204), (900602.0, 827, 31317), (903223.0, 973, 28956), (907925.0, 366, 47458), (930249.0, 125, 83204), (930249.0, 500, 41602), (930249.0, 605, 37820), (954809.0, 355, 50676), (1024001.0, 645, 40320), (1039681.0, 490, 46968), (1039681.0, 640, 41097), (1098305.0, 594, 45064), (1159172.0, 703, 43719), (1197901.0, 682, 45870), (1201887.0, 497, 53912), (1204353.0, 113, 113296), (1204353.0, 452, 56648), (1280001.0, 761, 46400), (1294299.0, 854, 44290), (1524095.0, 429, 73584), (1555849.0, 925, 51156), (1574351.0, 598, 64380), (1618804.0, 535, 69987), (1625626.0, 467, 75225), (1653751.0, 453, 77700), (1850887.0, 428, 89466), (1907162.0, 587, 78717), (2024999.0, 295, 117900), (2143295.0, 94, 221064), (2143295.0, 376, 110532), (2143295.0, 846, 73688), (2271050.0, 699, 85899), (2281249.0, 73, 267000), (2281249.0, 292, 133500), (2281249.0, 657, 89000), (2376415.0, 329, 131016), (2499849.0, 173, 190060), (2499849.0, 692, 95030), (2535751.0, 460, 118230), (2550251.0, 750, 93122), (2588599.0, 133, 224460), (2588599.0, 532, 112230), (2862251.0, 430, 138030), (2989440.0, 479, 136591), (3034565.0, 934, 99294), (3287049.0, 389, 166660), (3505951.0, 636, 139020), (3674890.0, 251, 231957), (3678725.0, 534, 159194), (3844063.0, 217, 260952), (3844063.0, 868, 130476), (3959299.0, 274, 239190), (4120901.0, 918, 136010), 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(2178548422.0, 778, 78104745)] # print(max(generateBlindly())) # print(sorted(generateBlindly(), reverse=True)) # print(regularContinuedFractionToFraction(getRepeatingRegContFrac(7)[:-1])) ds = [d for d in range(2, 1001) if not sqrt(d).is_integer()] candidates = [] for d in ds: i = 1 regContFrac = getRepeatingRegContFrac(d) frac = regularContinuedFractionToFraction(regContFrac[:i]) x, y = frac.numerator, frac.denominator erg = x ** 2 - d * y ** 2 while erg != 1: i += 1 if i > len(regContFrac): regContFrac = regContFrac + regContFrac[1:] frac = regularContinuedFractionToFraction(regContFrac[:i]) x, y = frac.numerator, frac.denominator erg = x ** 2 - d * y ** 2 # (x,d,y) print((frac.numerator, d, frac.denominator, erg)) candidates.append((frac.numerator, d, frac.denominator)) print(max(candidates))
def testRegularContinuedFractionToFraction1_15(self):
self.assertEqual(Fraction(1, 15), regularContinuedFractionToFraction([0, 15]))
def getMagicNumbers(count=10): result = [2] a, b = divmod(count - 1, 3) triples = [(1, 2 * i, 1) for i in range(1, a + 1)] result = result + list(reduce(lambda t1, t2 : t1 + t2, triples)) if b == 1: result.append(1) elif b == 2: result = result + [1, 2 * (a + 1)] return result def magic(magicNumbers): return magicNumbers[0] + \ reduce( lambda accumulator, nextMagicNumber: Fraction(1, nextMagicNumber + accumulator), reversed(magicNumbers[1:]), 0) def oldMagic(magicNumbers): if len(magicNumbers) == 1: return Fraction(1, magicNumbers[0]) return Fraction(1, magicNumbers[0] + magic(magicNumbers[1:])) if __name__ == '__main__': print(sum([int(ch) for ch in str(regularContinuedFractionToFraction(getMagicNumbers(100)).numerator)])) print(magic(getMagicNumbers())) print(sum([int(ch) for ch in str(magic(getMagicNumbers(100)).numerator)]))
