380
The smallest squares containing k 380's :
38025 = 1952,
3803805625 = 616752,
38071380380401 = 61702012.
3802 = 144400, with 144 = 122 and 400 = 202.
16815k + 19285k + 53295k + 55005k are squares for k = 1,2,3 (3802, 807502, 181583002).
Komachi Square Sum : 3802 = 12 + 52 + 422 + 892 + 3672.
3802 + 3812 + 3822 + ... + 99792 = 5755602.
Page of Squares : First Upload January 17, 2005 ; Last Revised March 4, 2011by Yoshio Mimura, Kobe, Japan
381
The smallest squares containing k 381's :
238144 = 4882,
381381841 = 195292,
381933812938129 = 195431272.
8890k + 12446k + 23368k + 100457k are squares for k = 1,2,3 (3812, 1042672, 320805812).
3-by-3 magic squares consisting of different squares with constant 3812:
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3812 = 145161, 14 + 5 + 1 + 61 = 92,
3812 = 145161, 14 + 5 + 16 + 1 = 62.
3812 = 73 + 233 + 513 = 83 + 303 + 493.
Page of Squares : First Upload January 17, 2005 ; Last Revised March 4, 2011by Yoshio Mimura, Kobe, Japan
382
The smallest squares containing k 382's :
53824 = 2322,
3823938244 = 618382,
382113826343824 = 195477322.
3822 = 145924, 1 + 45 * 9 - 24 = 382.
18145k + 22729k + 50233k + 54817k are squares for k = 1,2,3 (3822, 798382, 175838422).
3822 = 145924, 1 + 4 + 5 + 9 + 2 + 4 = 52,
3822 = 145924, 1 + 4 + 5924 = 772,
3822 = 145924, 1 + 459 + 24 = 222.
3822 = 145924 appears in the decimal expression of e:
e = 2.71828•••145924••• (from the 17906th digit)
by Yoshio Mimura, Kobe, Japan
383
The smallest squares containing k 383's :
138384 = 3722,
3833838724 = 619182,
3830538338343649 = 618913432.
3832 = 146689, a square with a non-decreasing digits.
3-by-3 magic squares consisting of different squares with constant 3832:
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3832 = 146689, 1 + 466 + 8 + 9 = 222,
3832 = 146689, 14 + 66 + 89 = 132,
3832 = 146689, 146 + 6 + 8 + 9 = 132.
(13 + 23 + ... + 983)(993 + 1003 + ... + 2243)(2253 + 2263 + ... + 3833) = 82871536920482.
Page of Squares : First Upload January 17, 2005 ; Last Revised February 23, 2009by Yoshio Mimura, Kobe, Japan
384
The smallest squares containing k 384's :
3844 = 622,
384238404 = 196022,
38438412816384 = 61998722.
The squares which begin with 384 and end in 384 are
38466192384 = 1961282, 384241296384 = 6198722, 384558736384 = 6201282,
384861418384 = 6203722, 3840141898384 = 19596282,...
1 / 384 = 0.0026041666..., 22 + 62 + 02 + 42 + 162 + 62 + 62 = 384.
202 + 384 = 282, 202 - 384 = 42.
Komachi equation: 3842 = 12 / 22 / 32 * 42 * 562 / 72 * 82 * 92.
3842 is the 4th square which is the sum of 9 seventh powers.
3842 = 147456, 14 + 7 + 4 + 5 + 6 = 62,
3842 = 147456, 14 + 7 + 4 + 56 = 92,
3842 = 147456, 14 + 74 + 56 = 122.
3842 = 163 + 323 + 483.
Page of Squares : First Upload January 17, 2005 ; Last Revised July 22, 2011by Yoshio Mimura, Kobe, Japan
385
The smallest squares containing k 385's :
33856 = 1842,
38503858176 = 1962242,
38566385313856 = 62101842.
385 = 12 + 22 + ... + 102.
3852 = (132 + 6)(292 + 6).
3852 = 282 + 292 + 302 + 312 + ... + 772.
3852 is the 5th square which is the sum of 7 sixth powers : 1, 2, 4, 4, 6, 6, 6.
3852 + 3862 + 3872 + ... + 52222 = 52232 + 52242 + 52252 + ... + 65792.
385k + 1232k + 2156k + 2156k are squares for k = 1,2,3 (772, 33112, 1482252).
3-by-3 magic squares consisting of different squares with constant 3852:
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3852 = 148225, 14 + 8 + 2 + 25 = 72,
3852 = 148225, 14 + 8 + 22 + 5 = 72,
3852 = 148225, 14 + 82 + 25 = 112,
3852 = 148225, 14 + 822 + 5 = 292.
(13 + 23 + ... + 153)(163 + 173 + ... + 213)(223 + 233 + ... + 3853) = 17599982402.
(13 + 23 + ... + 1443)(1453 + 1463 + ... + 1933)(1943 + 1953 + ... + 3853) = 116659515772802.
3852 = 148225 appears in the decimal expression of π:
π = 3.14159•••148225••• (from the 95333rd digit).
by Yoshio Mimura, Kobe, Japan
386
The smallest squares containing k 386's :
386884 = 6222,
38638656 = 62162,
3861638603863056 = 621420842.
3862 + 1 is a prime number.
3862 = 1442 + 2422 + 2642 : 4622 + 2422 + 4412 = 6832.
Page of Squares : First Upload July 10, 2006 ; Last Revised August 17, 2013by Yoshio Mimura, Kobe, Japan
387
The smallest squares containing k 387's :
338724 = 5822,
27538738704 = 1659482,
1387497387763876 = 372491262.
3872 = 1432 + 2422 + 2662 : 6622 + 2422 + 3412 = 7832.
3872± 2 are primes.
3-by-3 magic squares consisting of different squares with constant 3872:
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3872 = 149769, 1 + 4 + 9 + 7 + 6 + 9 = 62,
3872 = 149769, 143 + 93 + 73 + 63 + 93 = 692,
3872 = 149769, 149 + 7 + 69 = 152.
25026k + 30444k + 40377k + 53922k are squares for k = 1,2,3 (3872, 780452, 163248212).
3872 = 149769 appears in the decimal expression of e:
e = 2.71828•••149769••• (from the 37464th digit)
by Yoshio Mimura, Kobe, Japan
388
The smallest squares containing k 388's :
38809 = 1972,
23883538849 = 1545432,
1388038893883236 = 372563942.
Komachi Fraction : 3882 = 8129376 / 54.
Komachi equations:
3882 = - 14 + 24 + 34 + 44 * 54 - 64 + 74 - 84 - 94 = - 94 - 84 + 74 - 64 + 54 * 44 + 34 + 24 - 14.
3882 = 84 + 124 + 124 + 184.
3882 = 150544, 1 + 5 + 0 + 54 + 4 = 82,
3882 = 150544, 1 + 50 + 5 + 4 + 4 = 82,
3882 = 150544, 1 + 50 + 5 + 44 = 102,
3882 = 150544, 15 + 0 + 5 + 44 = 82.
by Yoshio Mimura, Kobe, Japan
389
The smallest squares containing k 389's :
389376 = 6242,
3891389161 = 623812,
389389157838916 = 197329462.
3892 = 151321, 15 * 13 * 2 - 1 = 389.
3892 = 992 + 2642 + 2682 : 8622 + 4622 + 992 = 9832.
3-by-3 magic squares consisting of different squares with constant 3892:
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3892 = 151321, 152 + 12 + 32 + 212 = 262,
3892 = 151321, 15 + 1 + 32 + 1 = 72,
3892 = 151321, 15 + 13 + 21 = 72.
522 + 532 + 542 + 552 + ... + 3892 = 44332.
(12 + 22 + ... + 62)(72 + 82 + ... + 392)(402 + 412 + ... + 3892) = 60510452.
(13 + 23 + ... + 1433)(1443 + 1453 + ... + 3893) = 7737752882.
Page of Squares : First Upload January 17, 2005 ; Last Revised August 17, 2013by Yoshio Mimura, Kobe, Japan