Subject: Squares consisted of 3 different digits: Solutions up to 10^50
   Date: Wed, 12 May 2004 02:45:29 +0200
   From: "tatar" 
     To: kc2h-msm@asahi-net.or.jp

Dear Hisanori,

    I think that you might be intersted in this. All calculations were done on celeron 633MHz, it took about 6 days.
I programmed it in C, using "quad-double / double-double computation package by Yozo Hida, Xiaoye S. Li and David H. Bailey".
Also for some special cases code can be optimized to reduce using of types from mentioned library, and core thing can be done
only using double type (directly supported by coprocessor). With these optimizations I think that some patterns can be test
up to 10^64 for ~15 days. I will certainly perform few more calculations probably soon, hope so.

    milos tatarevic

	  S	  O-MAX				A				 	 D		sqrt(A)

123,	 3888  	  25
	
				311323333121312322332133323111223321313321	 	42	557963558954625926861
124,    12248     56
				144222411144424121442444112111142224442244	 	42	379766258564954821662
125,	13608	  56
				15522211212125512112255222511252122511225	 	41	124588166420914599285
				22515511252551552115222525221211511125225	 	41	150051695267169681235
				1212222122255221215111111512151155125251522225   	46	34816980372445012123335
				1215155515521525522215211555521512552151515552225	49	1102340925268369741032335
126,	 6768	  34
127,	 3888     27
128,	 5832	  31
129,	 7776	  36
134,	 5192	  30
136,	10112	  46
138,	 1944     14
				81838388131883313833383381811133318888113813881  	47	286074095527510693610891
145,	 3704     25
146,	16088	  64
				141166141116611464114116414644641441611664	 	42	375720828696801774892
				644111614414444441664646611416446114664441	 	42	802565644925350914229
				16411146144166666464466464146441416441444416	 	44	4051067284576580130696
				116411111611641646616166611414441166144111616	 	45	10789398111648380852704
147,	 5096	  27
				4741471777144414774147714111744447747417744	 	43	2177492084289725902412
148,	13232	  55
				1814141111418481411488184148411114184811141884841	49	1346900557360669225841779
149,	 5904	  33
156,	 9632 	  44
				66615611661661666651111615111161616151161	 	41	258100003219026842869
				5511661555161166511651661611666516615516655616	 	46	74240565428619726479296
158,	 1944     17
				5818888111118115811551585855811558551185881	 	43	2412237158970509643109
167,	 9488	  43
168,	 8984	  42
				186188166186668818681818186188818861116816	 	42	431495267861269619604
				1168116111686616811868118886618818666111186868681	49	1080794204132598414568541
169,	13472	  61
				169661969919699919691616999616691969199169	 	42	411900436901564744737
				1166199961991666696199696161116991961919696969   	46	34149670012924966713187
178,	 1944	  16
189,	 3888     24
234,	 5648	  30
235,	 9720	  45
236,	 2608	  18
239,	 3888     23
245,	15960	  64
				2455442524452554445254444455245254424242244	 	43	1566985170463509665838
				25224555254424242244454444254455442544542225	 	44	5022405325580985229335
				25424554524455524225542255422225542555555225	 	44	5042276720337304556485
				24524252545545555425452252442555424225445255225  	47	156602211177063382566485
				224245452455222424254455242452522555442545442244 	48	473545618135383472428338			
246,	 9456	  42
				64244464242642246466444266646244264622246244	 	44	8015264452445860907338
				2442426662442422262266222264624646466242442242624	49	1562826497869300353470568
247,	 5200     29
248,	 6816     36
				2884842244828242284244242842824284482242248484   	46	53710727465081333454522
				4282482824288222284288288882288482848444822888484	49	2069416058768323727702022
249,	12280	  54
				49492229242429222429494944494949499949249	 	41	222468490448488507807
				299492994242299992492444422992424244422244	 	42	547259530974381470838
256,	29012    117
				52266222626626566662522622656666222265625	 	41	228618071522411733125
				56525226222626252566552565525652262562265225625  	47	237750344316525128700475
				266556625655662226525525225552225265562566256225 	48	516291221749568609228465			
257,	 9720     45
258,	 9720     43
259,	13608	  61
				2555525222555995255555255252529952995599225	 	43	1598601020441309256565
267,	 3552	  23
269,	 5968     33
				2262629269629662226292666922999622262992962929	 	46	47567102808870567435673
279,	 3888     25
289,	 5832	  33
345,	 3120	  19
346,	 8032     39
347,	 4544     27
				3477773374437343773773333743737447337433344	 	43	1864878916830083039312
348,	 5936     31
				34884384443343843348888488484833488344838384443844	50	5906300402396058566810062
349,	 4936     27
				34449444994349999433343349994949439344449	 	41	185605616817891584607
356,	 6176	  31
367,	 6432     33
368,	 2912	  19
369,	10512 	  48
				339666666363999366939366969366969936633336969	 	45	18430047920827535573187
389,	 1944     18
456,	 9264     42
				56456464454655444665444666454556666644544	 	41	237605691124298293112
				5665455455445656566644565645546455454464446464	 	46	75269219840819770294592
				456644564666666555445565455644644555565545646656 	48	675754811056988742949784
457,	 3024	  20
458,	 6000	  31
459,	 3960	  25
				495555459949459999994555545994544549499995545449 	48	703957001491895099962643
467,	 7088     36
				664676644466466777446466766667744446667647467664 	48	815277035409723028858892
468,	10704	  48	
469,	15640	  65
				999994646649499499946646996649944649464969	 	42	999997323321167445187
				494464664969644944649644494946666694449496996	 	45	22236561446627600040614
				94444646994669646646646969664664969996646496669696	50	9718263579193026119075264
478,	 5936	  30
479,	 4936	  29
489,	13872	  65
567,	 5088	  30
				777666657567776675657756675676567555755556	 	42	881854102200458483334
				6565656667556566576676575665776756666556676	 	43	2562353735836753390526
568,	 2128	  19
569,	 9632	  44
589,	 1944	  17
678,	 2896	  20
679,	10080     48
689,	 9240	  44
				6698696669868698868988986669668968886668689	 	43	2588184048685235767383
789,	 1944	  18


> 10^50:


(w3 < 18)
2-5-6	
	6626226562522666562566262626266252566552622656522256	52	81401637345465395512991484