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2400 - 2499

2400

502 + 2400 = 702, 502 - 2400 = 102.

Komachi equation: 24002 = 92 * 82 / 72 / 62 * 52 * 42 / 32 * 2102.

Page of Squares : First Upload September 21, 2010 ; Last Revised July 27, 2011
by Yoshio Mimura, Kobe, Japan

2401

The square of 49.

24012 = 5764801, a square with different digits.

24012 = 77 + 77 + 77 + 77 + 77 + 77 + 77.

665k + 1421k + 2401k + 5117k are squares for k = 1,2,3 (982, 58662, 3885702).

Komachi equations:
24012 = 124 * 34 / 44 + 564 * 74 / 84 - 94 = 124 * 34 / 44 * 564 * 74 / 84 / 94
 = - 124 * 34 / 44 + 564 * 74 / 84 + 94.

Page of Squares : First Upload April 16, 2007 ; Last Revised May 17, 2011
by Yoshio Mimura, Kobe, Japan

2402

24022 = 14 + 74 + 74 + 494.

24022 = 5769604, and 576 = 242, 9604 = 982.

Page of Squares : First Upload April 16, 2007 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2404

The square root of 2404 is 49.030602..., 49 = 02 + 32 + 02 + 62 + 02 + 22.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2405

S2(2405) = S2(1474) + S2(2204), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2406

24062 = 973 + 1313 + 1383.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2407

24072 = 24 + 264 + 264 + 474.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2408

24072 = (62 + 7)(72 + 7)(492 + 7).

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

2409

24092 = 5803281, a zigzag square.

24092 = 5803281, and 5 * 80 * 3 * 2 + 8 + 1 = 2409.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2414

24142 = 5827396, a zigzag square with different digits.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2415

Komachi equations:
24152 = 12 * 232 / 42 * 52 / 62 * 72 * 82 * 92 = 122 * 3452 * 62 * 72 / 82 / 92.

Page of Squares : First Upload April 16, 2007 ; Last Revised September 21, 2010
by Yoshio Mimura, Kobe, Japan

2417

24172 = 44 + 144 + 144 + 494.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2418

24184 = 34184181532176, and 32 + 42 + 182 + 412 + 82 + 152 + 32 + 22 + 12 + 72 + 62 = 2418,
24184 = 34184181532176, and 32 + 412 + 82 + 42 + 182 + 152 + 32 + 22 + 12 + 72 + 62 = 2418.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

2421

The square root of 2421 is 49.2036..., 49 = 22 + 02 + 32 + 62.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2424

24242 = 403 + 1323 + 1523.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2425

24252 = 923 + 1053 + 1583 = 204 + 304 + 304 + 454.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2426

24262 = 5885476, and 5 * 8 + 85 * 4 * 7 + 6 = 2426.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2428

24282 = 124 + 224 + 244 + 484.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2430

24302 = 723 + 813 + 1713 = 37 + 67 + 67 + 67 + 67 + 97.

24302 = (22 + 5)(52 + 5)(72 + 5)(202 + 5).

Page of Squares : First Upload July 22, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

2432

The square root of 2432 is 49.315312..., 49 = 32 + 12 + 52 + 32 + 12 + 22.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2434

24342 = 5924356, 52 + 92 + 22 + 42 + 32 + 52 + 62 = 142.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2435

24352 = 5929225, a square with just 3 kinds of digits.

24352 = 5929225, and 5929 = 772, 225 = 152.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2436

24362 = 5934096, a zigzag square.

24362 = 84 + 304 + 404 + 404.

Page of Squares : First Upload April 16, 2007 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2439

24392 = 5948721, a square with different digits.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2440

24402 = (22 + 4)(222 + 4)(392 + 4).

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

2441

24412 = 5958481, a zigzag square.

1 / 2441 = 0.0004096... and 4096 = 642.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2444

24442 = 5973136, a square with odd digits except the last digit 6.

24442± 3 are primes.

Page of Squares : First Upload August 24, 2013 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

2447

24472 = 153 + 1053 + 1693.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2448

24482 = 5992704, 52 + 92 + 92 + 22 + 72 + 02 + 42 = 162.

24482 = 5992704, and 5 + 9 + 9 * 270 + 4 = 2448.

24482 = (12 + 8)(22 + 8)(42 + 8)(482 + 8) = (22 + 8)(32 + 8)(82 + 8)(202 + 8)
= (32 + 8)(42 + 8)(82 + 8)(142 + 8) = (42 + 8)(102 + 8)(482 + 8) = (82 + 8)(142 + 8)(202 + 8).

24482 = 84 + 164 + 284 + 484 = 124 + 244 + 244 + 484.

Page of Squares : First Upload April 16, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

2450

24502 = 354 + 354 + 354 + 354.

24502 = (12 + 6)(22 + 6)(132 + 6)(222 + 6) = (82 + 6)(132 + 6)(222 + 6).

14k + 1162k + 1274k + 2450k are squares for k = 1,2,3 (702, 29962, 1354362).

Page of Squares : First Upload July 22, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

2454

24542 = S2(176) + S2(232), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2456

24562 = 6031936, a zigzag square.

24562 = 793 + 1133 + 1603.

Page of Squares : First Upload April 16, 2007 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2457

24572 = 6036849, and
6 + 0 + 3 + 68 * 4 * 9 = 6 - 0 + 3 + 68 * 4 * 9 = 6 + 03 + 68 * 4 * 9 = 2457.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2458

24582 = 753 + 813 + 1723.

1 / 2458 = 0.000406834825, 42 + 02 + 62 + 82 + 32 + 482 + 22 + 52 = 2458,
1 / 2458 = 0.000406834825, 42 + 062 + 82 + 32 + 482 + 22 + 52 = 2458.

Page of Squares : First Upload April 16, 2007 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2460

24602 = 6051600, and 60 * 51 - 600 = 2460.

2460k + 2490k + 3930k + 9345k are squares for k = 1,2,3 (1352, 107252, 9524252).

Page of Squares : First Upload April 16, 2007 ; Last Revised May 17, 2011
by Yoshio Mimura, Kobe, Japan

2461

24612 = 75 + 175 + 175 + 205.

A cubic polynomial :
(X + 3632)(X + 13642)(X + 20162) = X3 + 24612X2 + 28882922X + 9981861122.

Page of Squares : First Upload April 16, 2007 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2462

24622 = 6061444, 62 + 02 + 62 + 12 + 42 + 42 + 42 = 112.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2464

24642 = (12 + 7)(22 + 7)(72 + 7)(352 + 7) = (22 + 7)(212 + 7)(352 + 7) = (72 + 7)(92 + 7)(352 + 7).

A cubic polynomial :
(X + 11282)(X + 24642)(X + 228692) = X3 + 230292X2 + 620355122X + 635619156482.

24642 = 6071296 appears in the decimal expressions of e:
  e = 2.71828•••6071296••• (from the 83159th digit)

Page of Squares : First Upload April 16, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

2465

2291k + 2465k + 2755k + 5945k are squares for k = 1,2,3 (1162, 73662, 5079642).

Page of Squares : First Upload May 17, 2011 ; Last Revised May 17, 2011
by Yoshio Mimura, Kobe, Japan

2466

24662 = (131+132+133)2 + (134+135+136)2 + (137+138+139)2 + ... + (200+201+202)2.

Page of Squares : First Upload April 16, 2007 ; Last Revised April 16, 2007
by Yoshio Mimura, Kobe, Japan

2469

Komachi equation: 24692 = 98762 / 52 * 42 / 322 * 102.

Page of Squares : First Upload September 21, 2010 ; Last Revised September 21, 2010
by Yoshio Mimura, Kobe, Japan

2470

24702 = 55 + 125 + 155 + 185 + 205.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2472

24722 = 133 + 723 + 1793 = 264 + 264 + 384 + 424.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2476

24762 = 6130576 appears in the decimal expressions of π:
  π = 3.14159•••6130576••• (from the 69571st digit)

Page of Squares : First Upload November 4, 2008 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

2477

Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
2477 - 6505 - 4250 - 4264 - ... - 7186 - 12437 - 1946 - 2477
(Note f(2477) = 242 + 772 = 6505,   f(6505) = 652 + 052 = 4250, etc. See 1946)

24775 = 93245961804076157 : 92 + 32 + 22 + 452 + 92 + 62 + 12 + 82 + 02 + 42 + 02 + 72 + 62 + 12 + 52 + 72 = 2477.

24772 = 6135529 appears in the decimal expressions of π:
  π = 3.14159•••6135529••• (from the 56957th digit)

Page of Squares : First Upload October 9, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

2478

24782 = 473 + 1093 + 1683 = 493 + 663 + 1793.

882k + 2478k + 16338k + 24402k are squares for k = 1,2,3 (2102, 294842, 43482602).

Page of Squares : First Upload July 22, 2008 ; Last Revised May 17, 2011
by Yoshio Mimura, Kobe, Japan

2482

24822 = 6160324, a zigzag square.

24822 = 94 + 214 + 214 + 494.

Page of Squares : First Upload April 16, 2007 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2484

24842 = 183 + 333 + 1833.

24845 = 94570994818151424 : 92 + 42 + 52 + 72 + 02 + 92 + 92 + 42 + 82 + 12 + 82 + 152 + 12 + 422 + 42 = 2484.

Page of Squares : First Upload July 22, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

2485

24852 = 6175225, 62 + 12 + 72 + 52 + 22 + 22 + 52 = 122.

24852 + 24862 + 24872 + ... + 25202 = 25212 + 25222 + 25232 + ... + 25552.

Page of Squares : First Upload April 16, 2007 ; Last Revised September 13, 2011
by Yoshio Mimura, Kobe, Japan

2486

24862± 3 are primes.

Page of Squares : First Upload January 16, 2014 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

2488

24882± 3 are primes.

24882 = 45 + 125 + 125 + 145 + 225.

Page of Squares : First Upload July 22, 2008 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

2490

2460k + 2490k + 3930k + 9345k are squares for k = 1,2,3 (1352, 107252, 9524252).

Page of Squares : First Upload May 17, 2011 ; Last Revised May 17, 2011
by Yoshio Mimura, Kobe, Japan

2493

24932 = 6215049, a square with different digits.

24932 = 993 + 1153 + 1553.

Page of Squares : First Upload April 16, 2007 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2496

24962 = 83 + 1843.

Page of Squares : First Upload July 22, 2008 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2497

24972 = 15 + 25 + 85 + 165 + 225.

24972 = (184 + 185)2 + (186 + 187)2 + (188 + 189)2 + ... + (248 + 249)2.

Page of Squares : First Upload April 16, 2007 ; Last Revised July 22, 2008
by Yoshio Mimura, Kobe, Japan

2498

24982 = 6240004, a square with even digits.

24982± 3 are primes.

Page of Squares : First Upload April 16, 2007 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan