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To help with the testing data, here are the corresponding fractions for n = 3, k = 1:
(253, 451, 23, 41) (297, 495, 27, 45) (398, 597, 38, 57) (390, 975, 30, 75) (496, 992, 46, 92) (199, 796, 19, 76) (693, 990, 63, 90) (187, 781, 17, 71) (891, 990, 81, 90) (395, 790, 35, 70) (396, 792, 36, 72) (597, 995, 57, 95) (396, 495, 36, 45) (392, 980, 32, 80) (583, 781, 53, 71) (493, 986, 43, 86) (596, 894, 56, 84) (216, 864, 21, 84) (594, 792, 54, 72) (495, 792, 45, 72) (191, 955, 11, 55) (286, 583, 26, 53) (270, 756, 20, 56) (462, 660, 42, 60) (268, 469, 28, 49) (136, 340, 16, 40) (796, 995, 76, 95) (149, 894, 14, 84) (297, 891, 27, 81) (156, 858, 16, 88) (176, 770, 16, 70) (242, 341, 22, 31) (168, 672, 18, 72) (198, 594, 18, 54) (363, 660, 33, 60) (176, 275, 16, 25) (136, 238, 16, 28) (396, 891, 36, 81) (199, 995, 19, 95) (286, 385, 26, 35) (451, 550, 41, 50) (299, 897, 29, 87) (335, 737, 35, 77) (473, 572, 43, 52) (299, 598, 29, 58) (394, 985, 34, 85) (597, 796, 57, 76) (352, 451, 32, 41) (134, 938, 14, 98) (194, 970, 14, 70) (160, 640, 10, 40) (671, 770, 61, 70) (266, 665, 26, 65) (163, 652, 13, 52) (149, 596, 14, 56) (217, 775, 21, 75) (385, 583, 35, 53) (427, 976, 42, 96) (536, 938, 56, 98) (132, 231, 12, 21) (187, 385, 17, 35) (154, 550, 14, 50) (346, 865, 34, 85) (594, 990, 54, 90) (275, 671, 25, 61) (187, 484, 17, 44) (490, 980, 40, 80) (234, 936, 24, 96) (682, 781, 62, 71) (394, 591, 34, 51) (536, 737, 56, 77) (187, 880, 17, 80) (374, 473, 34, 43) (781, 880, 71, 80) (196, 294, 16, 24) (385, 484, 35, 44) (298, 596, 28, 56) (737, 938, 77, 98) (335, 938, 35, 98) (305, 854, 30, 84) (164, 656, 14, 56) (154, 451, 14, 41) (198, 891, 18, 81) (154, 253, 14, 23) (143, 242, 13, 22) (199, 597, 19, 57) (385, 781, 35, 71) (196, 980, 16, 80) (286, 682, 26, 62) (249, 498, 24, 48) (186, 465, 18, 45) (253, 352, 23, 32) (169, 676, 19, 76) (199, 398, 19, 38) (195, 975, 15, 75) (176, 671, 16, 61) (264, 660, 24, 60) (297, 693, 27, 63) (572, 671, 52, 61) (138, 345, 18, 45) (165, 660, 15, 60) (491, 982, 41, 82) (176, 473, 16, 43) (396, 693, 36, 63) (165, 363, 15, 33) (484, 781, 44, 71) (133, 532, 13, 52) (196, 490, 16, 40) (385, 880, 35, 80) (693, 792, 63, 72) (197, 591, 17, 51) (286, 880, 26, 80) (341, 440, 31, 40) (286, 781, 26, 71) (178, 979, 18, 99) (143, 440, 13, 40) (484, 682, 44, 62) (396, 594, 36, 54) (167, 668, 17, 68) (363, 462, 33, 42) (298, 894, 28, 84) (275, 473, 25, 43) (594, 693, 54, 63) (119, 595, 11, 55) (193, 965, 13, 65) (275, 572, 25, 52) (112, 616, 12, 66) (146, 365, 14, 35) (161, 644, 11, 44) (187, 286, 17, 26) (198, 396, 18, 36) (291, 970, 21, 70) (392, 490, 32, 40) (363, 561, 33, 51) (792, 990, 72, 90) (198, 990, 18, 90) (162, 648, 12, 48) (268, 670, 28, 70) (294, 490, 24, 40) (233, 932, 23, 92) (397, 794, 37, 74) (296, 592, 26, 52) (198, 495, 18, 45) (132, 330, 12, 30) (398, 995, 38, 95) (399, 798, 39, 78) (498, 996, 48, 96) (561, 660, 51, 60) (275, 374, 25, 34) (134, 737, 14, 77) (176, 374, 16, 34) (374, 770, 34, 70) (494, 988, 44, 88) (196, 392, 16, 32) (198, 297, 18, 27) (462, 561, 42, 51) (572, 770, 52, 70) (396, 990, 36, 90) (306, 765, 30, 75) (121, 220, 11, 20) (260, 650, 20, 50) (335, 536, 35, 56) (197, 394, 17, 34) (134, 335, 14, 35) (165, 264, 15, 24) (192, 960, 12, 60) (165, 561, 15, 51) (473, 770, 43, 70) (190, 950, 10, 50) (264, 462, 24, 42) (469, 670, 49, 70) (106, 265, 10, 25) (183, 732, 18, 72) (224, 728, 24, 78) (386, 965, 38, 95) (187, 682, 17, 62) (374, 671, 34, 61) (176, 572, 16, 52) (116, 464, 11, 44) (143, 341, 13, 31) (495, 891, 45, 81) (130, 325, 10, 25) (495, 990, 45, 90) (594, 891, 54, 81) (352, 550, 32, 50) (139, 695, 13, 65) (297, 990, 27, 90) (499, 998, 49, 98) (332, 830, 32, 80) (484, 880, 44, 80) (591, 985, 51, 85) (473, 671, 43, 61) (693, 891, 63, 81) (264, 561, 24, 51) (179, 895, 17, 85) (275, 770, 25, 70) (295, 590, 25, 50) (286, 484, 26, 44) (598, 897, 58, 87) (792, 891, 72, 81) (583, 682, 53, 62) (134, 536, 14, 56) (149, 298, 14, 28) (385, 682, 35, 62) (226, 565, 22, 55) (532, 931, 52, 91) (166, 664, 16, 64) (297, 792, 27, 72) (349, 698, 34, 68) (195, 390, 15, 30) (242, 440, 22, 40) (294, 392, 24, 32) (194, 291, 14, 21) (297, 396, 27, 36) (197, 985, 17, 85) (484, 583, 44, 53) (264, 363, 24, 33) (159, 795, 15, 75) (262, 655, 22, 55) (497, 994, 47, 94) (249, 996, 24, 96) (198, 792, 18, 72) (253, 550, 23, 50) (449, 898, 44, 88) (583, 880, 53, 80) (198, 693, 18, 63) (231, 330, 21, 30) (297, 594, 27, 54) (495, 594, 45, 54) (294, 980, 24, 80) (133, 931, 13, 91) (238, 340, 28, 40) (398, 796, 38, 76) (165, 462, 15, 42) (334, 835, 34, 85) (492, 984, 42, 84) (374, 572, 34, 52) (682, 880, 62, 80) (154, 352, 14, 32) (495, 693, 45, 63) (187, 583, 17, 53)
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Project Euler #33: Digit canceling fractions
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To help with the testing data, here are the corresponding fractions for n = 3, k = 1: