940
The smallest squares containing k 940's :
9409 = 972,
9409194001 = 970012,
894004199409409 = 298999032.
by Yoshio Mimura, Kobe, Japan
941
The smallest squares containing k 941's :
1094116 = 10462,
13941941776 = 1180762,
1081941094194129 = 328928732.
3-by-3 magic squares consisting of different squares with constant 9412:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(12, 261, 904, 384, 824, 243, 859, 372, 96), | (13, 96, 936, 576, 741, 68, 744, 572, 69), |
(36, 132, 931, 364, 861, 108, 867, 356, 84), | (36, 229, 912, 453, 804, 184, 824, 432, 141), |
(40, 216, 915, 645, 660, 184, 684, 635, 120), | (69, 252, 904, 616, 696, 147, 708, 581, 216), |
(76, 372, 861, 483, 756, 284, 804, 419, 252), | (84, 480, 805, 645, 616, 300, 680, 525, 384), |
(96, 499, 792, 603, 576, 436, 716, 552, 261), | (99, 436, 828, 492, 684, 419, 796, 477, 156), |
(176, 411, 828, 576, 708, 229, 723, 464, 384), | (216, 453, 796, 499, 744, 288, 768, 356, 411) |
Page of Squares : First Upload February 13, 2006 ; Last Revised October 30, 2009
by Yoshio Mimura, Kobe, Japan
942
The smallest squares containing k 942's :
94249 = 3072,
19423439424 = 1393682,
1362942194294209 = 369180472.
(13 + 23 + ... + 5523)(5533 + 5543 + ... + 9423) = 636619019402.
1 / 942 = 0.0010615711252...,
and 12 + 062 + 152 + 72 + 12 + 12 + 252 + 22 = 942.
498k + 942k + 3138k + 3522k are squares for k = 1,2,3 (902, 48362, 2748602).
The 4-by-4 magic squares consisting of different squares with constant 942:
|
|
|
9422 = 887364, 8 + 8 + 7 + 3 + 6 + 4 = 62,
9422 = 887364, 88 + 73 + 64 = 152,
9422 = 887364, 887 + 3 + 6 + 4 = 302.
by Yoshio Mimura, Kobe, Japan
943
The smallest squares containing k 943's :
394384 = 6282,
18943943769 = 1376372,
999439431943744 = 316139122.
9432 = 112 + 4622 + 8222 : 2282 + 2642 + 112 = 3492.
3-by-3 magic squares consisting of different squares with constant 9432:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(6, 402, 853, 587, 666, 318, 738, 533, 246), | (27, 538, 774, 606, 603, 398, 722, 486, 363), |
(42, 331, 882, 389, 798, 318, 858, 378, 101), | (42, 453, 826, 507, 686, 402, 794, 462, 213), |
(43, 438, 834, 654, 587, 342, 678, 594, 277), | (66, 267, 902, 603, 682, 246, 722, 594, 123), |
(70, 318, 885, 357, 830, 270, 870, 315, 182), | (90, 507, 790, 645, 610, 318, 682, 510, 405), |
(110, 315, 882, 630, 682, 165, 693, 570, 290), | (123, 246, 902, 398, 837, 174, 846, 358, 213), |
(123, 438, 826, 574, 693, 282, 738, 466, 357), | (133, 306, 882, 522, 763, 186, 774, 462, 277), |
(258, 549, 722, 578, 678, 309, 699, 358, 522) |
9432 = 889249, 8 + 8 + 92 + 4 + 9 = 112.
Page of Squares : First Upload February 13, 2006 ; Last Revised August 17, 2013by Yoshio Mimura, Kobe, Japan
944
The smallest squares containing k 944's :
44944 = 2122,
11494412944 = 1072122,
165944944969444 = 128819622.
The squares which begin with 944 and end in 944 are
94425914944 = 3072882, 944224210944 = 9717122, 944371916944 = 9717882,
9441559034944 = 30727122, 9442026092944 = 30727882,...
(13 + 23 + ... + 6043)(6053 + 6063 + ... + 9043)(9053 + 9063 + ... + 9443) = 118910702813100002.
9442 = 891136, 8 + 9 + 11 + 36 = 82,
9442 = 891136, 89 + 1 + 1 + 3 + 6 = 102,
9442 = 891136, 89 + 1136 = 352.
by Yoshio Mimura, Kobe, Japan
945
The smallest squares containing k 945's :
379456 = 6162,
594579456 = 243842,
94569459450489 = 97246832.
9452 is the ninth square which is the sum of 5 fifth powers : 65 + 65 + 95 + 95 + 155.
9452 = 893025 : 8 + 930 + 2 + 5 = 945.
9452 = 893025, a square with different digits.
9452 = (42 + 5)(102 + 5)(202 + 5) = (42 - 1)(2442 - 1).
Komachi equations:
9452 = 122 * 32 * 42 * 52 / 62 * 72 / 82 * 92 = 122 * 32 * 452 * 62 * 72 / 82 / 92.
9452 + 9462 + 9472 + ... + 115282 = 7144622.
9452 = 423 + 663 + 813 = 333 + 563 + 883.
(1 + 2 + ... + 6)(7 + 8 + ... + 20)(21 + 22 + ... + 29) = 9452,
(1)(2 + 3 + ... + 43)(44 + 45 + ... + 61) = 9452,
(1 + 2)(3 + 4 + 5 + 6 + 7 )(8 + 9 + ... + 154) = 9452.
3-by-3 magic squares consisting of different squares with constant 9452:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(4, 97, 940, 503, 796, 80, 800, 500, 55), | (4, 272, 905, 545, 740, 220, 772, 521, 160), |
(8, 220, 919, 425, 820, 200, 844, 415, 92), | (9, 288, 900, 612, 684, 225, 720, 585, 180), |
(17, 344, 880, 400, 800, 305, 856, 367, 160), | (20, 95, 940, 215, 916, 88, 920, 212, 41), |
(20, 95, 940, 464, 820, 73, 823, 460, 64), | (20, 215, 920, 640, 680, 145, 695, 620, 160), |
(20, 380, 865, 488, 745, 316, 809, 440, 212), | (20, 380, 865, 640, 631, 292, 695, 592, 244), |
(20, 607, 724, 640, 524, 457, 695, 500, 400), | (30, 165, 930, 267, 894, 150, 906, 258, 75), |
(30, 165, 930, 510, 786, 123, 795, 498, 114), | (30, 330, 885, 426, 795, 282, 843, 390, 174), |
(30, 330, 885, 645, 654, 222, 690, 597, 246), | (30, 510, 795, 645, 570, 390, 690, 555, 330), |
(31, 92, 940, 260, 905, 80, 908, 256, 55), | (40, 151, 932, 580, 740, 95, 745, 568, 124), |
(40, 248, 911, 655, 664, 152, 680, 625, 200), | (40, 580, 745, 655, 520, 440, 680, 535, 380), |
(41, 520, 788, 620, 580, 415, 712, 535, 316), | (55, 340, 880, 500, 737, 316, 800, 484, 137), |
(55, 340, 880, 628, 671, 220, 704, 572, 265), | (66, 363, 870, 555, 690, 330, 762, 534, 165), |
(68, 500, 799, 535, 680, 380, 776, 425, 332), | (70, 245, 910, 350, 854, 203, 875, 322, 154), |
(70, 350, 875, 490, 763, 266, 805, 434, 238), | (72, 279, 900, 396, 828, 225, 855, 360, 180), |
(75, 438, 834, 570, 645, 390, 750, 534, 213), | (75, 570, 750, 654, 510, 453, 678, 555, 354), |
(80, 260, 905, 316, 863, 220, 887, 284, 160), | (80, 335, 880, 520, 752, 239, 785, 464, 248), |
(80, 335, 880, 608, 656, 305, 719, 592, 160), | (80, 520, 785, 568, 655, 376, 751, 440, 368), |
(95, 244, 908, 460, 808, 169, 820, 425, 200), | (95, 380, 860, 548, 680, 361, 764, 535, 152), |
(95, 380, 860, 580, 704, 247, 740, 503, 304), | (95, 460, 820, 580, 620, 415, 740, 545, 220), |
(104, 535, 772, 572, 580, 479, 745, 520, 260), | (145, 424, 832, 640, 568, 401, 680, 625, 200), |
(148, 311, 880, 415, 820, 220, 836, 352, 265), | (150, 498, 789, 555, 690, 330, 750, 411, 402), |
(150, 555, 750, 618, 510, 501, 699, 570, 282), | (160, 436, 823, 620, 673, 236, 695, 500, 400), |
(160, 620, 695, 649, 580, 368, 668, 415, 524), | (215, 536, 748, 620, 652, 289, 680, 425, 500), |
(215, 568, 724, 620, 460, 545, 680, 599, 268) |
The 4-by-4 magic squares consisting of different squares with constant 945:
|
|
9452 = 893025, 8 + 9 + 302 + 5 = 182,
9452 = 893025, 89 + 30 + 25 = 122,
9452 = 893025, 893 + 0 + 2 + 5 = 302.
9452 = 893025 appears in the decimal expression of e:
e = 2.71828•••893025••• (from the 59442nd digit)
by Yoshio Mimura, Kobe, Japan
946
The smallest squares containing k 946's :
946729 = 9732,
3694694656 = 607842,
2946946344494656 = 542857842.
9462 = 894916, a zigzag square.
9462 = 4022 + 4242 + 7442 : 4472 + 4242 + 2042 = 6492.
9462 = 513 + 723 + 733.
Page of Squares : First Upload February 13, 2006 ; Last Revised August 17, 2013by Yoshio Mimura, Kobe, Japan
947
The smallest squares containing k 947's :
329476 = 5742,
2947947025 = 542952,
394700947194724 = 198670822.
9472 = 896809, a zigzag square.
Komachi square sum : 9472 = 22 + 72 + 82 + 1562 + 9342.
1 / 947 = 0.00 1 0 5 5 9 6 6 2 0 9 0 8 1 3 0 9 3 9 8 0 9 9 2 6 0 8 2 3 6 5 3,
and the sum of the squares of its digits is 947.
3-by-3 magic squares consisting of different squares with constant 9472:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(6, 97, 942, 657, 678, 74, 682, 654, 63), | (15, 178, 930, 578, 735, 150, 750, 570, 97), |
(15, 470, 822, 522, 690, 385, 790, 447, 270), | (18, 574, 753, 666, 543, 398, 673, 522, 414), |
(38, 273, 906, 447, 794, 258, 834, 438, 97), | (38, 399, 858, 561, 682, 342, 762, 522, 209), |
(38, 447, 834, 561, 718, 258, 762, 426, 367), | (63, 466, 822, 542, 657, 414, 774, 498, 223), |
(66, 182, 927, 223, 906, 162, 918, 207, 106), | (70, 465, 822, 570, 678, 335, 753, 470, 330), |
(90, 447, 830, 655, 570, 378, 678, 610, 255), | (102, 286, 897, 546, 753, 178, 767, 498, 246), |
(102, 498, 799, 609, 578, 438, 718, 561, 258), | (146, 447, 822, 543, 718, 294, 762, 426, 367), |
(162, 591, 722, 641, 462, 522, 678, 578, 321), | (207, 398, 834, 466, 783, 258, 798, 354, 367) |
9472 = 896809, 8 + 96 + 8 + 0 + 9 = 112.
Page of Squares : First Upload February 13, 2006 ; Last Revised October 30, 2009by Yoshio Mimura, Kobe, Japan
948
The smallest squares containing k 948's :
94864 = 3082,
948948025 = 308052,
859489948409481 = 293170592.
9482 = 898704 is an exchangeable square (870489 = 9332).
9482 + 0782 = 904788.
9482 = 898704, 8 + 9 + 8 + 7 + 0 + 4 = 62,
9482 = 898704, 8 + 9 + 8 + 704 = 272.
by Yoshio Mimura, Kobe, Japan
949
The smallest squares containing k 949's :
894916 = 9462,
68794994944 = 2622882,
1949294994974041 = 441508212.
168172 = 1972 + 1982 + 1992 + ... + 9492.
3-by-3 magic squares consisting of different squares with constant 9492:
A2 | B2 | C2 |
D2 | E2 | F2 |
G2 | H2 | K2 |
where (A, B, C, D, E, F, G, H, K) = | |
(0, 365, 876, 624, 660, 275, 715, 576, 240), | (13, 156, 936, 216, 912, 149, 924, 211, 48), |
(13, 156, 936, 504, 792, 139, 804, 499, 72), | (21, 288, 904, 456, 796, 243, 832, 429, 156), |
(21, 312, 896, 392, 819, 276, 864, 364, 147), | (27, 364, 876, 516, 741, 292, 796, 468, 219), |
(48, 309, 896, 621, 688, 204, 716, 576, 237), | (51, 148, 936, 468, 819, 104, 824, 456, 117), |
(68, 141, 936, 264, 904, 117, 909, 252, 104), | (76, 240, 915, 435, 824, 180, 840, 405, 176), |
(76, 357, 876, 411, 804, 292, 852, 356, 219), | (84, 472, 819, 616, 651, 312, 717, 504, 364), |
(104, 468, 819, 576, 621, 428, 747, 544, 216), | (141, 572, 744, 616, 624, 363, 708, 429, 464), |
(156, 429, 832, 464, 768, 309, 813, 356, 336), | (156, 572, 741, 603, 636, 364, 716, 411, 468), |
(211, 516, 768, 636, 653, 264, 672, 456, 491) |
9492 = 900601, 9 + 0 + 0 + 6 + 0 + 1 = 42,
9492 = 900601, 900 + 60 + 1 = 312.
by Yoshio Mimura, Kobe, Japan