950
The smallest squares containing k 950's :
559504 = 7482,
9504495081 = 974912,
9509507895001 = 30837492.
9502 + 9512 + 9522 + ... + 132482 = 8802572.
(12 + 22 + ... + 3002)(3012 + 3022 + ... + 9242)(9252 + 9262 + ... + 9502) = 2292920175002.
The 4-by-4 magic square consisting of different squares with constant 950:
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Page of Squares : First Upload February 20, 2006 ; Last Revised October 30, 2009
by Yoshio Mimura, Kobe, Japan
951
The smallest squares containing k 951's :
1595169 = 12632,
9519514624 = 975682,
209514595195161 = 144746192.
Komachi cube sum : 9512 = 53 + 73 + 83 + 123 + 463 + 933.
(13 + 23 + ... + 7763)(7773 + 7783 + ... + 9513) = 1018024156802.
3-by-3 magic squares consisting of different squares with constant 9512:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(2, 179, 934, 466, 814, 157, 829, 458, 86), | (2, 179, 934, 586, 746, 67, 749, 562, 166), |
(2, 194, 931, 586, 733, 154, 749, 574, 118), | (9, 168, 936, 648, 684, 129, 696, 639, 108), |
(14, 541, 782, 637, 586, 394, 706, 518, 371), | (19, 178, 934, 262, 899, 166, 914, 254, 67), |
(19, 418, 854, 574, 686, 323, 758, 509, 266), | (26, 326, 893, 542, 739, 254, 781, 502, 206), |
(26, 563, 766, 598, 586, 451, 739, 494, 338), | (29, 154, 938, 658, 674, 131, 686, 653, 86), |
(33, 396, 864, 576, 696, 297, 756, 513, 264), | (35, 470, 826, 670, 574, 355, 674, 595, 310), |
(46, 173, 934, 509, 794, 122, 802, 494, 131), | (67, 206, 926, 586, 739, 122, 746, 562, 179), |
(74, 163, 934, 221, 914, 142, 922, 206, 109), | (74, 430, 845, 605, 674, 290, 730, 515, 326), |
(86, 298, 899, 557, 746, 194, 766, 509, 242), | (98, 461, 826, 646, 574, 397, 691, 602, 254), |
(109, 614, 718, 662, 466, 499, 674, 557, 374), | (144, 492, 801, 648, 639, 276, 681, 504, 432), |
(154, 334, 877, 371, 838, 254, 862, 301, 266), | (156, 441, 828, 612, 684, 249, 711, 492, 396), |
(158, 394, 851, 499, 766, 262, 794, 403, 334), | (166, 562, 749, 614, 509, 518, 707, 574, 274), |
(206, 418, 829, 466, 781, 278, 803, 346, 374), | (250, 499, 770, 530, 730, 301, 749, 350, 470) |
9512 = 904401 appears in the decimal expression of π:
π = 3.14159•••904401••• (from the 81690th digit).
by Yoshio Mimura, Kobe, Japan
952
The smallest squares containing k 952's :
79524 = 2822,
1829529529 = 427732,
74589529529529 = 86365232.
(12 + 22 + ... + 1042)(1052)(1062 + 1072 + ... + 9522) = 10983472502.
(13 + 23 + ... + 8323)(8333 + 8342 + ... + 9523) = 1014426067202.
9522 = 906304, 9 + 0 + 6 + 30 + 4 = 72,
9522 = 906304, 90 + 6 + 304 = 202.
9522 = 906304 appears in the decimal expression of e:
e = 2.71828•••906304••• (from the 56417th digit).
by Yoshio Mimura, Kobe, Japan
953
The smallest squares containing k 953's :
59536 = 2442,
495329536 = 222562,
39953953795396 = 63209142.
9532 = 4312 + 4322 + 7322 : 2372 + 2342 + 1342 = 3592.
Komachi fraction : 9532 = 65391048 / 72.
3-by-3 magic squares consisting of different squares with constant 9532:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(12, 233, 924, 584, 732, 177, 753, 564, 152), | (12, 252, 919, 368, 849, 228, 879, 352, 108), |
(17, 96, 948, 276, 908, 87, 912, 273, 44), | (17, 492, 816, 564, 663, 388, 768, 476, 303), |
(24, 528, 793, 633, 584, 408, 712, 537, 336), | (28, 177, 936, 663, 676, 108, 684, 648, 143), |
(28, 432, 849, 471, 732, 388, 828, 431, 192), | (72, 296, 903, 647, 648, 264, 696, 633, 152), |
(72, 487, 816, 537, 696, 368, 784, 432, 327), | (80, 303, 900, 465, 800, 228, 828, 420, 215), |
(87, 324, 892, 604, 672, 303, 732, 593, 144), | (145, 528, 780, 660, 620, 297, 672, 495, 460), |
(152, 399, 852, 591, 712, 228, 732, 492, 361), | (156, 297, 892, 408, 836, 207, 847, 348, 264) |
9532 = 908209, 9 + 0 + 82 + 0 + 9 = 102.
Page of Squares : First Upload February 20, 2006 ; Last Revised August 17, 2013by Yoshio Mimura, Kobe, Japan
954
The smallest squares containing k 954's :
95481 = 3092,
954995409 = 309032,
1954995495439561 = 442153312.
9542 = (26 + 27 + 28)2 + (29 + 30 + 31)2 + (32 + 33 + 34)2 + ... + (95 + 96 + 97)2.
(541 / 954)2 = 0.321586479... (Komachic).
Komachi square sum : 9542 = 32 + 72 + 92 + 4212 + 8562.
The 4-by-4 magic squares consisting of different squares with constant 954:
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Page of Squares : First Upload February 20, 2006 ; Last Revised October 30, 2009
by Yoshio Mimura, Kobe, Japan
955
The smallest squares containing k 955's :
695556 = 8342,
9559559529 = 977732,
95559559558849 = 97754572.
9552 is the fifth squares which is the sum of 10 seventh powers.
3-by-3 magic squares consisting of different squares with constant 9552:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(26, 393, 870, 510, 730, 345, 807, 474, 190), | (30, 215, 930, 345, 870, 190, 890, 330, 105), |
(30, 215, 930, 505, 786, 198, 810, 498, 89), | (30, 215, 930, 615, 726, 82, 730, 582, 201), |
(30, 345, 890, 386, 810, 327, 873, 370, 114), | (30, 345, 890, 615, 674, 282, 730, 582, 201), |
(30, 505, 810, 615, 630, 370, 730, 510, 345), | (54, 422, 855, 478, 729, 390, 825, 450, 170), |
(55, 210, 930, 390, 855, 170, 870, 370, 135), | (55, 390, 870, 618, 649, 330, 726, 582, 215), |
(82, 201, 930, 474, 818, 135, 825, 450, 170), | (98, 414, 855, 630, 615, 370, 711, 602, 210), |
(105, 190, 930, 270, 903, 154, 910, 246, 153), | (105, 330, 890, 406, 825, 258, 858, 350, 231), |
(105, 330, 890, 630, 694, 183, 710, 567, 294), | (105, 566, 762, 630, 615, 370, 710, 462, 441), |
(135, 370, 870, 422, 810, 279, 846, 345, 278), | (135, 370, 870, 642, 681, 190, 694, 558, 345), |
(162, 359, 870, 534, 762, 215, 775, 450, 330), | (162, 510, 791, 665, 630, 270, 666, 505, 462) |
9552 = 912025, and 9 = 32, 1 = 12, 2025 = 152.
9552 = 912025, 91 + 2 + 0 + 2 + 5 = 102,
9552 = 912025, 91 + 2025 = 462.
by Yoshio Mimura, Kobe, Japan
956
The smallest squares containing k 956's :
17956 = 1342,
3379561956 = 581342,
201956329565956 = 142111342.
The squares which begin with 956 and end in 956 are
956221913956 = 9778662, 956746121956 = 9781342, 9561292673956 = 30921342,
9562727477956 = 30923662, 9564385057956 = 30926342,...
9562 = 913936, a square with odd digits except the last digit 6.
Komachi equation : 9562 = - 96 + 86 + 76 + 66 + 56 + 46 - 36 - 26 + 106.
9562 + 9572 + 9582 + ... + 10512 = 98362,
9562 + 9572 + 9582 + ... + 16772 = 358152,
9562 + 9572 + 9582 + ... + 32832 = 1072822,
9562 + 9572 + 9582 + ... + 1139012 = 221938892,
9562 + 9572 + 9582 + ... + 1222052 = 246646752.
9562 = 913936, 9 + 13 + 93 + 6 = 112,
9562 = 913936, 913 + 936 = 432.
by Yoshio Mimura, Kobe, Japan
957
The smallest squares containing k 957's :
1495729 = 12232,
108495795769 = 3293872,
6957195736957636 = 834098062.
9572 = 1122 + 4132 + 8562 : 6582 + 3142 + 2112 = 7592,
9572 = 1162 + 4932 + 8122 : 2182 + 3942 + 6112 = 7592.
The square root of 957 is 30. 9 3 5 4 16 5 9 6 5 16 0 3 9 ...,
and 302 = 92 + 32 + 52 + 42 + 162 + 52 + 92 + 62 + 52 + 162 + 02 + 32 + 92.
3-by-3 magic squares consisting of different squares with constant 9572:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(8, 157, 944, 277, 904, 148, 916, 272, 53), | (8, 508, 811, 608, 629, 388, 739, 512, 328), |
(18, 378, 879, 447, 774, 342, 846, 417, 162), | (28, 304, 907, 427, 808, 284, 856, 413, 112), |
(29, 232, 928, 472, 811, 188, 832, 452, 139), | (29, 232, 928, 512, 788, 181, 808, 491, 148), |
(42, 234, 927, 522, 783, 174, 801, 498, 162), | (43, 260, 920, 580, 725, 232, 760, 568, 125), |
(52, 211, 932, 659, 668, 188, 692, 652, 109), | (53, 332, 896, 448, 784, 317, 844, 437, 112), |
(56, 227, 928, 268, 896, 203, 917, 248, 116), | (56, 637, 712, 668, 536, 427, 683, 472, 476), |
(63, 486, 822, 606, 657, 342, 738, 498, 351), | (76, 437, 848, 587, 692, 304, 752, 496, 323), |
(80, 395, 868, 640, 668, 245, 707, 560, 320), | (81, 258, 918, 522, 783, 174, 798, 486, 207), |
(92, 424, 853, 664, 643, 248, 683, 568, 356), | (109, 388, 868, 532, 749, 268, 788, 452, 301), |
(116, 493, 812, 532, 644, 467, 787, 508, 196), | (136, 412, 853, 512, 757, 284, 797, 416, 328), |
(148, 524, 787, 557, 692, 356, 764, 403, 412), | (172, 533, 776, 587, 556, 512, 736, 568, 227), |
(203, 464, 812, 556, 728, 277, 752, 413, 424), | (203, 464, 812, 592, 707, 256, 724, 448, 437) |
9572 = 915849, 9 + 1 + 5 + 8 + 4 + 9 = 62,
9572 = 915849, 9 + 1 + 58 + 4 + 9 = 92,
9572 = 915849, 9 + 15 + 8 + 49 = 92,
9572 = 915849, 915 + 849 = 422.
9572 = 915849 appears in the decimal expression of e:
e = 2.71828•••915849••• (from the 10170th digit),
(915849 is the ninth 6-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
958
The smallest squares containing k 958's :
29584 = 1722,
6958395889 = 834172,
2495807958795844 = 499580622.
9582 = 917764, 9 + 177 + 6 + 4 = 142,
9582 = 917764, 91 + 7 + 7 + 64 = 132,
9582 = 917764, 917 + 764 = 412.
9582 = 917764 appears in the decimal expression of π:
π = 3.14159•••917764••• (from the 65824th digit).
by Yoshio Mimura, Kobe, Japan
959
The smallest squares containing k 959's :
295936 = 5442,
32995995904 = 1816482,
279599599597824 = 167212322.
9592 = 919681, a zigzag square.
9592 = 1142 + 4542 + 8372 = 7382 + 4542 + 4112.
3-by-3 magic squares consisting of different squares with constant 9592:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(5, 234, 930, 666, 670, 165, 690, 645, 166), | (6, 138, 949, 507, 806, 114, 814, 501, 78), |
(6, 347, 894, 459, 786, 302, 842, 426, 171), | (18, 194, 939, 426, 843, 166, 859, 414, 102), |
(22, 354, 891, 549, 726, 302, 786, 517, 186), | (27, 94, 954, 346, 891, 78, 894, 342, 59), |
(27, 366, 886, 626, 678, 261, 726, 571, 258), | (50, 366, 885, 534, 725, 330, 795, 510, 166), |
(54, 363, 886, 402, 814, 309, 869, 354, 198), | (54, 454, 843, 491, 738, 366, 822, 411, 274), |
(58, 186, 939, 309, 894, 158, 906, 293, 114), | (58, 606, 741, 654, 517, 474, 699, 534, 382), |
(69, 166, 942, 282, 906, 139, 914, 267, 114), | (69, 562, 774, 654, 594, 373, 698, 501, 426), |
(84, 399, 868, 672, 644, 231, 679, 588, 336), | (94, 261, 918, 594, 738, 149, 747, 554, 234), |
(114, 437, 846, 549, 666, 418, 778, 534, 171), | (114, 454, 837, 571, 642, 426, 762, 549, 194), |
(117, 554, 774, 606, 558, 491, 734, 549, 282), | (139, 318, 894, 474, 806, 213, 822, 411, 274), |
(150, 491, 810, 590, 690, 309, 741, 450, 410), | (198, 626, 699, 661, 414, 558, 666, 597, 346) |
9592 = 919681, and 9 = 32, 196 = 142, 81 = 92.
9592 = 919681, 91 + 9 + 68 + 1 = 132,
9592 = 919681, 91 + 96 + 8 + 1 = 142,
9592 = 919681, 919 + 681 = 402.
by Yoshio Mimura, Kobe, Japan