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[原创] 特殊平方数(含3种数字!且不包含零的)

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发表于 2012-8-27 14:34:54 | 显示全部楼层 |阅读模式

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{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}
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2012-8-27 14:35:37 | 显示全部楼层
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. ]
复制代码
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2012-8-27 14:40:25 | 显示全部楼层
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}
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2012-8-27 14:41:12 | 显示全部楼层
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*) ]
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2017-1-23 16:53:36 | 显示全部楼层
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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