平方组成数
显然0,1,4,9是0,1,2,3的平方注意到 144组成数字是1,4,4，且是12的平方
441，10404，40401也是
请问，是否还有数字具有
1、是某个整数的平方
2、10进制表示由0,1,4,9组成 由12*10^n 102*10^n 21*10^n 201*10^n组成的数字的平方都是这个性质
还有其他形式么？ A058414Squares composed of digits {0,1,4}, not ending with zero.
1, 4, 144, 441, 1444, 10404, 40401, 1004004, 1100401, 4004001, 100040004, 114041041, 400040001, 414041104, 10000400004, 10110101401, 40000400001, 41011110144, 141001001001, 414441100441, 1000004000004, 1041110041104
A019544Squares whose digits are squares.
0, 1, 4, 9, 49, 100, 144, 400, 441, 900, 1444, 4900, 9409, 10000, 10404, 11449, 14400, 19044, 40000, 40401, 44100, 44944, 90000, 144400, 419904, 490000, 491401, 904401, 940900, 994009, 1000000
A061270Squares such that each digit is a square and the sum of the digits is a square.
1, 4, 9, 100, 144, 400, 441, 900, 10000, 10404, 14400, 40000, 40401, 44100, 44944, 90000, 1000000, 1004004, 1040400, 1440000, 4000000, 4004001, 4040100, 4410000, 4494400, 9000000, 9941409, 11909401, 100000000, 100040004, 100400400
更多的相关内容请点击：http://www.research.att.com/~njas/sequences/?q=441+10404+40401+square&sort=0&fmt=0&language=english&go=Search 呵呵
还有更高的么？ 这类数应该很容易被搜索到。 :lol
求出10^32内所有末位不是0的这类数字来 21^2 == 441
94925771^2 == 9010901999944441
446653271^2 == 199499144494999441
221454271^2 == 49041994144141441
632534119159521^2 == 400099411900911111419444949441
137843911871729^2 == 19000944040100991144149449441 下面列出10^32内，满足a^2=n，a的数字组成中不含0、n仅由{0,1,4,9}数字组成的n：
21^2 == 441
12^2 == 144
38^2 == 1444
212^2 == 44944
4462^2 == 19909444
6357^2 == 40411449
31488^2 == 991494144
317712^2 == 100940914944
971643^2 == 944090119449
387288^2 == 149991994944
94925771^2 == 9010901999944441
446653271^2 == 199499144494999441
221454271^2 == 49041994144141441
211992712^2 == 44940909941114944
6356918988^2 == 40410419019994944144
33452129143^2 == 1119044944199949914449
11832751643^2 == 140014011444919199449
64738643362712^2 == 4191091944444414491191994944
31481612751643^2 == 991091941444411141999199449
33318312524788^2 == 1110109949499444911114444944
632534119159521^2 == 400099411900911111419444949441
137843911871729^2 == 19000944040100991144149449441
3315269143525771^2 == 10991009494014099194444941144441
3176649241589462^2 == 10091100404090904111144149449444
2224645859254893^2 == 4949049199099941194941144441449
9536294568877893^2 == 90940914104409999119141144119449
一位的数就不列出了。
[ 本帖最后由 medie2005 于 2008-12-16 13:31 编辑 ]
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