特殊平方数（含3种数字！且不包含零的）

mathematica

{169,13}
{196,14}
{256,16}
{289,17}
{324,18}
{361,19}
{529,23}
{576,24}
{625,25}
{729,27}
{784,28}
{841,29}
{961,31}
{1156,34}
{1225,35}
{1521,39}
{1681,41}
{2116,46}
{3136,56}
{3364,58}
{3844,62}
{3969,63}
{4225,65}
{4489,67}
{4624,68}
{5625,75}
{5776,76}
{5929,77}
{6561,81}
{6889,83}
{7225,85}
{8281,91}
{8464,92}
{8836,94}
{11449,107}
{11664,108}
{12321,111}
{14161,119}
{14641,121}
{14884,122}
{16641,129}
{17161,131}
{19881,141}
{26244,162}
{27225,165}
{28224,168}
{35344,188}
{37636,194}
{41616,204}
{46656,216}
{48841,221}
{55696,236}
{56644,238}
{65536,256}
{66564,258}
{68644,262}
{69169,263}
{76176,276}
{93636,306}
{94249,307}
{97969,313}
{99225,315}
{111556,334}
{112225,335}
{114244,338}
{128881,359}
{136161,369}
{166464,408}
{212521,461}
{225625,475}
{228484,478}
{232324,482}
{235225,485}
{261121,511}
{265225,515}
{266256,516}
{276676,526}
{277729,527}
{332929,577}
{339889,583}
{442225,665}
{444889,667}
{446224,668}
{473344,688}
{499849,707}
{511225,715}
{525625,725}
{544644,738}
{553536,744}
{556516,746}
{585225,765}
{633616,796}
{646416,804}
{665856,816}
{695556,834}
{698896,836}
{767376,876}
{776161,881}
{797449,893}
{929296,964}
{1313316,1146}
{1336336,1156}
{1411344,1188}
{1418481,1191}
{1525225,1235}
{1666681,1291}
{2214144,1488}
{2217121,1489}
{2295225,1515}
{2424249,1557}
{2512225,1585}
{2621161,1619}
{2772225,1665}
{3323329,1823}
{3363556,1834}
{3553225,1885}
{3663396,1914}
{4439449,2107}
{4443664,2108}
{4545424,2132}
{4999696,2236}
{5112121,2261}
{5221225,2285}
{5345344,2312}
{5452225,2335}
{5555449,2357}
{5929225,2435}
{6441444,2538}
{6661561,2581}
{7447441,2729}
{8282884,2878}
{8868484,2978}
{8898289,2983}
{9229444,3038}
{9966649,3157}
{9991921,3161}
{11115556,3334}
{11122225,3335}
{11142244,3338}
{11282881,3359}
{11614464,3408}
{11771761,3431}
{13366336,3656}
{16966161,4119}
{22924944,4788}
{23299929,4827}
{26265625,5125}
{26646244,5162}
{27279729,5223}
{33235225,5765}
{34433424,5868}
{35545444,5962}
{42445225,6515}
{42994249,6557}
{44116164,6642}
{44422225,6665}
{44448889,6667}
{44462224,6668}
{45454564,6742}
{47444544,6888}
{47775744,6912}
{52229529,7227}
{56625625,7525}
{57577744,7588}
{66113161,8131}
{66699889,8167}
{85285225,9235}
{92294449,9607}
{111999889,10583}
{115111441,10729}
{121242121,11011}
{152152225,12335}
{165611161,12869}
{166616464,12908}
{227557225,15085}
{228281881,15109}
{252333225,15885}
{277722225,16665}
{337677376,18376}
{353665636,18806}
{363131136,19056}
{414488881,20359}
{421111441,20521}
{431434441,20771}
{434222244,20838}
{449948944,21212}
{525555625,22925}
{536663556,23166}
{544522225,23335}
{545549449,23357}
{552955225,23515}
{555356356,23566}
{556252225,23585}
{611919169,24737}
{645566464,25408}
{662444644,25738}
{664144441,25771}
{818188816,28604}
{966339396,31086}
{991494144,31488}
{996222969,31563}
{999444996,31614}
{1111155556,33334}
{1111222225,33335}
{1111422244,33338}
{1112822881,33359}
{1155252121,33989}
{1199998881,34641}
{1212919929,34827}
{1222551225,34965}
{1322122321,36361}
{1441113444,37962}
{1551414544,39388}
{1566655561,39581}
{1616361616,40204}
{1929229929,43923}
{1991212129,44623}
{2224254244,47162}
{2523555225,50235}
{2929299129,54123}
{2952292225,54335}
{3325252225,57665}
{3383399889,58167}
{3863368336,62156}
{4424245225,66515}
{4444222225,66665}
{4444488889,66667}
{4444622224,66668}
{4554225225,67485}
{4649466969,68187}
{4755757444,68962}
{4914991449,70107}
{4924249929,70173}
{5225121225,72285}
{5232352225,72335}
{5252625625,72475}
{5848884484,76478}
{6114614416,78196}
{6168688681,78541}
{6222212161,78881}
{6266622244,79162}
{6465446464,80408}
{6617171716,81346}
{6626611216,81404}
{6693366969,81813}
{6999999556,83666}
{7478444484,86478}
{9559559529,97773}
{9669968896,98336}
{15211522225,123335}
{16671716161,129119}
{17676766116,132954}
{26166621121,161761}
{26629996969,163187}
{26646644644,163238}
{27777222225,166665}
{36333696996,190614}
{43342243344,208188}
{44424414441,210771}
{44448445584,210828}
{49429294929,222327}
{53343445444,230962}
{54445222225,233335}
{55255554225,235065}
{59299555225,243515}
{59554545444,244038}
{63396693369,251787}
{64944444964,254842}
{65635365636,256194}
{66631613161,258131}
{66686864644,258238}
{69926926969,264437}
{72272257225,268835}
{78881777881,280859}
{88998998929,298327}
{96693633936,310956}
{111111555556,333334}
{111112222225,333335}
{111114222244,333338}
{111128222881,333359}
{111461164164,333858}
{132233322321,363639}
{149991994944,387288}
{213223221121,461761}
{242223434244,492162}
{255555525625,505525}
{265652622225,515415}
{344443393449,586893}
{422224444944,649788}
{433433939449,658357}
{441411414544,664388}
{443433464464,665908}
{444242245225,666515}
{444442222225,666665}
{444444888889,666667}
{444446222224,666668}
{466363336464,682908}
{611686666816,782104}
{648446888644,805262}
{669668898889,818333}
{686688996889,828667}
{696199996996,834386}
{756767765776,869924}
{883483443844,939938}
{949488489889,974417}
{989698666896,994836}
{1111166866161,1054119}
{1212225222121,1101011}
{1221126662116,1105046}
{1229129212921,1108661}
{1521115222225,1233335}
{1551155666116,1245454}
{1561665111556,1249666}
{1911961611169,1382737}
{2121112611216,1456404}
{2777772222225,1666665}
{2999882888289,1732017}
{3235555525225,1798765}
{4147177477444,2036462}
{4444667464644,2108238}
{5444452222225,2333335}
{5556363553636,2357194}
{5654446456464,2377908}
{5929599995929,2435077}
{5956596696996,2440614}
{6255626265625,2501125}
{6366366663556,2523166}
{7174474747441,2678521}
{9222293933329,3036823}
{9552259592929,3090673}
{9697699776769,3114113}
{9988488448849,3160457}
{11111115555556,3333334}
{11111122222225,3333335}
{11111142222244,3333338}
{11111282222881,3333359}
{11168168618161,3341881}
{11414343334144,3378512}
{13223121322321,3636361}
{13338133883881,3652141}
{18886681666161,4345881}
{21122122166161,4595881}
{21127711127121,4596489}
{25772527522225,5076665}
{31633661633161,5624381}
{39333932392329,6271677}
{43323224233444,6582038}
{43346343434436,6583794}
{44442422245225,6666515}
{44444422222225,6666665}
{44444448888889,6666667}
{44444462222224,6666668}
{44547775545744,6674412}
{46443434463364,6814942}
{48554584844544,6968112}
{49222249444449,7015857}
{58255285225225,7632515}
{64664242622464,8041408}
{84488488664644,9191762}
{86668968686689,9309617}
{88588285258225,9412135}
{92222199291121,9603239}
{99191919116196,9959514}
{99488994489889,9974417}

mathematica

Clear["Global`*"];(*Clear all variables*)
Do[ a=n^2;(*产生完全平方数*)
    b=Union@IntegerDigits@a;(*各个位的数,然后取并集*)
    If[ Length@b==3&&Min@b!=0,(*如果只包含两种数字,并且不包含零*)
        Print[{a,n}](*那么则打印这个整数和平方根*)
    ],
    {n,1,10^7} (*平方根的变化范围*)
]

代码如下：

1. Clear["Global`*"];(*Clear all variables*)
   
2. Do[ a=n^2;(*产生完全平方数*)
   
3.     b=Union@IntegerDigits@a;(*各个位的数,然后取并集*)
   
4.     If[ Length@b==3&&Min@b!=0,(*如果只包含两种数字,并且不包含零*)
   
5.         Print[{a,n}](*那么则打印这个整数和平方根*)
   
6.     ],
   
7.     {n,1,10^7} (*平方根的变化范围*)
   
8. ]
   
9. 
   

复制代码

mathematica

其中还算有意思的一些数（从后向前看）：
{169,13}
{196,14}
{256,16}
{289,17}
{324,18}
{361,19}
{529,23}
{576,24}
{625,25}
{729,27}
{784,28}
{841,29}
{961,31}
{1156,34}
{1225,35}
{1521,39}
{1681,41}
{2116,46}
{3136,56}
{3364,58}
{3844,62}
{3969,63}
{4225,65}
{4489,67}
{4624,68}
{5625,75}
{5776,76}
{6561,81}
{6889,83}
{7225,85}
{8281,91}
{8464,92}
{8836,94}
{14161,119}
{14641,121}
{14884,122}
{17161,131}
{19881,141}
{35344,188}
{48841,221}
{68644,262}
{97969,313}
{111556,334}
{112225,335}
{114244,338}
{261121,511}
{265225,515}
{332929,577}
{442225,665}
{444889,667}
{446224,668}
{473344,688}
{499849,707}
{553536,744}
{776161,881}
{1411344,1188}
{1418481,1191}
{2295225,1515}
{11115556,3334}
{11122225,3335}
{11142244,3338}
{44422225,6665}
{44448889,6667}
{44462224,6668}
{47444544,6888}
{52229529,7227}
{121242121,11011}
{449948944,21212}
{1111155556,33334}
{1111222225,33335}
{1111422244,33338}
{4444222225,66665}
{4444488889,66667}
{4444622224,66668}
{111111555556,333334}
{111112222225,333335}
{111114222244,333338}
{444442222225,666665}
{444444888889,666667}
{444446222224,666668}
{1212225222121,1101011}
{11111115555556,3333334}
{11111122222225,3333335}
{11111142222244,3333338}
{44444422222225,6666665}
{44444448888889,6666667}
{44444462222224,6666668}

mathematica

代码如下：

Clear["Global`*"];(*Clear all variables*)
Do[ a=n^2;(*产生完全平方数*)
    b=Union@IntegerDigits@a;(*各个位的数,然后取并集*)
    If[ Length@b==3&&Min@b!=0&&Length@Union@IntegerDigits@n==2,(*如果只包含两种数字,并且不包含零*)
        Print[{a,n}](*那么则打印这个整数和平方根*)
    ],
    {n,1,10^7} (*平方根的变化范围*)
]

manthanein

http://oeis.org/A235718