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3000 - 3099

3000

30002 = 1003 + 2003 = 633 + 1163 + 1933.

652 + 3000 = 852, 652 - 3000 = 352.

Page of Squares : First Upload August 4, 2008 ; Last Revised July 27, 2011
by Yoshio Mimura, Kobe, Japan

3001

30012 = 9006001, a reversible square (1006009 = 10032).

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3002

30022± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

3004

30045 = 244624325763841024 : 242 + 42 + 62 + 242 + 322 + 52 + 72 + 62 + 32 + 82 + 42 + 12 + 02 + 242 = 3004.

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

3005

30055 = 245031761259378125 : 242 + 52 + 02 + 32 + 12 + 72 + 62 + 122 + 52 + 92 + 372 + 82 + 12 + 252 = 242 + 52 + 02 + 32 + 12 + 72 + 62 + 12 + 252 + 92 + 372 + 82 + 122 + 52 = 3005.

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

3006

30062 = 10022 + 20042 + 20042 : 40022 + 40022 + 20012 = 60032.

Komachi equation: 30062 = 12 * 22 / 342 * 56782 * 92.

Page of Squares : First Upload September 28, 2010 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

3007

30072 = 1122 + 1132 + 1142 + 1152 + 1162 + ... + 3052.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3008

30082 = 2083 + 85 + 47.

Page of Squares : First Upload January 6, 2011 ; Last Revised January 6, 2011
by Yoshio Mimura, Kobe, Japan

3009

1 / 3009 = 0.0003323363243, 32 + 32 + 22 + 332 + 62 + 32 + 22 + 432 = 3009,
1 / 3009 = 0.0003323363243, 332 + 22 + 32 + 32 + 62 + 32 + 22 + 432 = 3009.

30092 = 10032 + 20062 + 20062 : 60022 + 60022 + 30012 = 90032.

4-cycle : 30092 = 09054081 -- 05402 = 00291600 -- 29162 = 08503056 -- 50302 = 25300900 (other examples : 1600 -- 5600 -- 3600 -- 9600 -- 1600, 2100 -- 4100 -- 8100 -- 6100 -- 2100).

Page of Squares : First Upload May 28, 2007 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

3010

2282k + 3010k + 3626k + 6958k are squares for k = 1,2,3 (1262, 87082, 6509162).

Page of Squares : First Upload May 27, 2011 ; Last Revised May 27, 2011
by Yoshio Mimura, Kobe, Japan

3011

30112 = 173 + 1023 + 2003 = 323 + 1533 + 1763.

30112 = 9066121, a reversible square (1216609 = 110322).

30112 = 9066121 appears in the decimal expressions of e:
  e = 2.71828•••9066121••• (from the 80895th digit)

Page of Squares : First Upload May 28, 2007 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

3014

12 + 22 + 32 + 42 + ... + 30142 = 9131131515, a square with odd digits
(the 4th 10-digit sum, and there are 4 such sums in all).

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3016

3016 = (12 + 22 + 32 + ... + 20152) / (12 + 22 + 32 + ... + 1392).

30162 = (22 + 4)(52 + 4)(1982 + 4) = (32 + 4)(102 + 4)(822 + 4).

30162 = 23 + 463 + 2083.

Page of Squares : First Upload August 4, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3018

30182 = 9108324, a square with different digits.

1 / 3018 = 0.0003313452617, 32 + 32 + 12 + 32 + 452 + 262 + 172 = 3018.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3020

S2(434) + S2(3017) = S2(3020), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3023

30232 = 34 + 124 + 284 + 544.

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

3024

752 + 3024 = 932, 752 - 3024 = 512.

30242 = (22 - 1)(82 - 1)(132 - 1)(172 - 1) = (72 - 1)(82 - 1)(552 - 1).

A cubic polynomial :
(X + 5312)(X + 8322)(X + 30242) = X3 + 31812X2 + 30172322X + 13359790082.

Komachi equations:
30242 = 12 / 22 * 32 * 42 * 5672 * 82 / 92 = 92 * 82 * 72 / 62 * 542 / 32 * 22 */ 12
 = 982 / 72 * 62 * 542 / 32 * 22 */ 12 = 92 / 82 * 72 * 62 * 52 * 42 * 322 / 102.

Page of Squares : First Upload May 28, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3025

The square of 55.

3025 = (30 + 25)2.

3025 is a zigzag square with different digits.

30252 = 223 + 223 + 2093 = 553 + 1653 + 1653.

Page of Squares : First Upload May 28, 2007 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

3026

30262 = 254 + 354 + 354 + 494.

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

3027

30272 = 9162729, a zigzag square.

30272 = 9162729, 92 + 12 + 62 + 22 + 72 + 22 + 92 = 162.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3028

30282 = 9168784, 9 * 1 * 6 * 8 * 7 + 8 - 4 = 3028.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3029

30292 = 9174841 , 9 * 1 * 7 * 48 + 4 + 1 = 3029.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3032

30322 = 1203 + 1303 + 1743.

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

3033

30332 = 10112 + 20222 + 20222 = 22022 + 22022 + 11012.

30332 = 274 + 364 + 364 + 484.

Page of Squares : First Upload August 4, 2008 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

3035

30355 = 257509631311896875 : 22 + 52 + 72 + 502 + 92 + 62 + 32 + 12 + 32 + 12 + 12 + 82 + 92 + 62 + 82 + 72 + 52 = 3035.

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

3036

30362 = 10122 + 20242 + 20242 : 42022 + 42022 + 21012 = 63032.

30362 = 9217296, 92 + 22 + 12 + 72 + 22 + 92 + 62 = 162.

Page of Squares : First Upload May 28, 2007 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

3037

30372 = 9223369, 9 + 2 + 2 + 336 * 9 = 9 + 2 * 2 + 336 * 9 = 3037.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3038

30382 = 9229444, a square with just 3 kinds of digits.

30382 = (372 + 3)(822 + 3).

154k + 3038k + 3626k + 9058k are squares for k = 1,2,3 (1262, 102202, 9049322).

Page of Squares : First Upload May 28, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3039

30392 = 10132 + 20262 + 20262 : 62022 + 62022 + 31012 = 93032.

The square root of 3039 is 55.1271...., and 55 = 12 + 22 + 72 + 12.

Page of Squares : First Upload May 28, 2007 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

3041

30412 = 9247681, a square with different digits.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3042

30422 = 394 + 394 + 394 + 394.

30422 = 9253764, a square with different digits.

30422 = (32 + 9)(7172 + 9).

The square root of 3042 is 55.15432..., and 55 = 12 + 52 + 42 + 32 + 22.

Page of Squares : First Upload May 28, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3043

The square root of 3043 is 55.1633, and 55 = 12 + 62 + 32 + 32.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3044

30442 = 9265936, a zigzag square.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3045

30452 = 9272025, a square pegged by 2.

3045k + 3381k + 4305k + 5145k are squares for k = 1,2,3 (1262, 81062, 5318462).

Page of Squares : First Upload May 28, 2007 ; Last Revised May 27, 2011
by Yoshio Mimura, Kobe, Japan

3047

30472 = 224 + 384 + 384 + 474.

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

3048

30482 = 9290304, a zigzag square.

30482 = 283 + 923 + 2043 = 323 + 1203 + 1963.

Page of Squares : First Upload May 28, 2007 ; Last Revised August 4, 2008
by Yoshio Mimura, Kobe, Japan

3050

30502 = 313 + 1013 + 2023 = 753 + 1453 + 1803 = 154 + 154 + 154 + 554.

30502 = 9302500, and 9 = 32, 302500 = 5502.

30502 = (12 + 1)(32 + 1)(6822 + 1) = (12 + 4)(13642 + 4).

Page of Squares : First Upload May 28, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3051

30512 = 663 + 813 + 2043.

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

3052

Komachi equation: 30522 = - 14 - 24 - 344 + 54 * 64 + 74 * 84 + 94.

Page of Squares : First Upload September 28, 2010 ; Last Revised September 28, 2010
by Yoshio Mimura, Kobe, Japan

3055

30552 = 9333025, 9 * 3 + 3 + 3025 = 3055.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3056

30562 = 9339136, a square with odd digits except the last digit 6.

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

3057

30572 = 55 + 125 + 135 + 155 + 245.

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

3059

30592 = 9357481, a square with different digits.

30592 = 13 -23 + 33 - 43 + 53 - 63 + 73 - ... + 2653.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3060

30602 = (12 + 9)(32 + 9)(52 + 9)(392 + 9).

30602 = 713 + 1293 + 1903.

12 + 22 + 32 + 42 + 52 + ... + 30602 = 9555554310, a square with non-increasing digits.

30602 = 15 x 16 + 16 x 17 + 17 x 18 + 18 x 19 + 19 x 20 + ...+ 303 x 304.

408k + 1156k + 2601k + 3060k are squares for k = 1,2,3 (852, 41992, 2187732).

Page of Squares : First Upload May 28, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3063

30632 = 9381969, a zigzag square.

30632 = 84 + 124 + 464 + 474.

30632 = 9381969, 9 * 38 * 1 * 9 - 6 - 9 = 3063.

30632 = 10212 + 20422 + 20422 : 24022 + 24022 + 12012 = 36032.

30635 = 269609371516851543 : 262 + 92 + 62 + 02 + 92 + 372 + 152 + 162 + 82 + 52 + 152 + 42 + 32 = 3063.

Page of Squares : First Upload May 28, 2007 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

3064

30642 = 9388096, 9 + 38 * 80 + 9 + 6 = 3064.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3066

30662± 5 are primes.

30662 = 10222 + 20442 + 20442 : 44022 + 44022 + 22012 = 66032.

762k + 1938k + 2334k + 3066k are squares for k = 1,2,3 (902, 43802, 2219402).

Page of Squares : First Upload May 27, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

3068

30682 = 453 + 1243 + 1953.

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

3069

30692 = 10232 + 20462 + 20462 : 64022 + 64022 + 32012 = 96032.

30692 = 642 + 652 + 662 + 672 + 682 + 692 + ... + 3052.

Page of Squares : First Upload May 28, 2007 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

3072

30722± 5 are primes.

30722 = 643 + 1283 + 1923.

Page of Squares : First Upload August 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

3075

30752 = 9455625, and 9 = 32, 455625 = 6752.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3076

30762± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

3077

1 / 3077 = 0.0003249..., and 3249 = 572.

1 / N = 0.000324... and 324 = 182 for N = 3077, 3078,..., 3086.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3078

30782 = (12 + 2)(42 + 2)(132 + 2)(322 + 2) = (12 + 2)(42 + 2)(52 + 2)(62 + 2)(132 + 2)
= (12 + 2)(62 + 2)(132 + 2)(222 + 2).

30785 = 276275947793014368 : 22 + 72 + 62 + 272 + 52 + 92 + 42 + 72 + 72 + 92 + 32 + 02 + 12 + 432 + 62 + 82 = 272 + 62 + 22 + 72 + 52 + 92 + 42 + 72 + 72 + 92 + 32 + 02 + 12 + 432 + 62 + 82 = 3078.

Komachi equations: 30782 = 92 / 82 * 762 * 542 / 32 * 22 */ 12.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3079

30792 = 783 + 1293 + 1903.

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

3081

30812± 2 are primes.

30812 + 30822 + 30832 + ... + 31202 = 31212 + 31222 + 31232 + ... + 31592.

Page of Squares : First Upload September 13, 2011 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

3084

30842 = 9511056, 92 + 52 + 12 + 12 + 02 + 52 + 62 = 132.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3087

30872 = 1473 + 1473 + 1473
= 24 + 364 + 384 + 494 = 144 + 284 + 424 + 494 = 214 + 424 + 424 + 424.

30872 is the 3rd square for which is the sum of 4 fourth powers in 3 ways:
    30872 = 24 + 364 + 384 + 494 = 144 + 284 + 424 + 494 = 214 + 424 + 424 + 424.

Komachi equations:
30872 = 982 * 72 * 62 * 52 / 42 * 32 * 22 / 102 = 982 * 72 * 62 / 52 / 42 * 32 / 22 * 102.

Page of Squares : First Upload May 28, 2007 ; Last Revised September 28, 2010
by Yoshio Mimura, Kobe, Japan

3088

30882 = 183 + 1263 + 1963.

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

3091

30912 = 9554281, and 92 + 52 + 542 + 22 + 82 + 12.

Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

3093

30932± 2 are primes.

30932 = 10312 + 20622 + 20622 : 26022 + 26022 + 13012 = 39032.

Page of Squares : First Upload September 18, 2013 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

3094

30942 = 9572836, a zigzag square with different digits.

Page of Squares : First Upload May 28, 2007 ; Last Revised May 28, 2007
by Yoshio Mimura, Kobe, Japan

3095

30952 = 1133 + 1243 + 1843.

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

3096

30962 = 10322 + 20642 + 20642 : 46022 + 46022 + 23012 = 69032.

30962 = (82 + 8)(112 + 8)(322 + 8).

A cubic polynomial :
(X + 30962)(X + 32252)(X + 44802) = X3 + 63292X2 + 223789202X + 447310080002.

Komachi equations:
30962 = 92 * 82 * 72 * 62 * 52 * 432 / 2102 = 92 * 82 / 72 / 62 / 52 * 432 * 2102.

30962 = 9585216 appears in the decimal expressions of e:
  e = 2.71828•••9585216••• (from the 50704th digit)

Page of Squares : First Upload May 28, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3097

30972 = 9591409, a zigzag square.

30972 = 24 + 224 + 464 + 474.

Page of Squares : First Upload May 28, 2007 ; Last Revised August 4, 2008
by Yoshio Mimura, Kobe, Japan

3098

30982 = 34 + 94 + 414 + 514 = 174 + 314 + 414 + 494.

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

3099

30992 = 10332 + 20662 + 20662 : 66022 + 66022 + 33012 = 99032.

Page of Squares : First Upload September 18, 2013 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan