2016年7月9日土曜日

160709(2)

Ruby


Numbers n such that 2 * n^2 - 1 is a square(3)

コードをシンプルにした。

n = 100
x, y = 1, 0
(n + 1).times{|i|
  x = 2 * y + x
  y = 2 * x + y
  a, b, c = (y - x - 1) / 2, (y - x + 1) / 2, x
  p [i, [a, b, c], a * a + b * b == c * c]
}

出力結果
[0, [0, 1, 1], true]
[1, [3, 4, 5], true]
[2, [20, 21, 29], true]
[3, [119, 120, 169], true]
[4, [696, 697, 985], true]
[5, [4059, 4060, 5741], true]
[6, [23660, 23661, 33461], true]
[7, [137903, 137904, 195025], true]
[8, [803760, 803761, 1136689], true]
[9, [4684659, 4684660, 6625109], true]
[10, [27304196, 27304197, 38613965], true]
[11, [159140519, 159140520, 225058681], true]
[12, [927538920, 927538921, 1311738121], true]
[13, [5406093003, 5406093004, 7645370045], true]
[14, [31509019100, 31509019101, 44560482149], true]
[15, [183648021599, 183648021600, 259717522849], true]
[16, [1070379110496, 1070379110497, 1513744654945], true]
[17, [6238626641379, 6238626641380, 8822750406821], true]
[18, [36361380737780, 36361380737781, 51422757785981], true]
[19, [211929657785303, 211929657785304, 299713796309065], true]
[20, [1235216565974040, 1235216565974041, 1746860020068409], true]
[21, [7199369738058939, 7199369738058940, 10181446324101389], true]
[22, [41961001862379596, 41961001862379597, 59341817924539925], true]
[23, [244566641436218639, 244566641436218640, 345869461223138161], true]
[24, [1425438846754932240, 1425438846754932241, 2015874949414289041], true]
[25, [8308066439093374803, 8308066439093374804, 11749380235262596085], true]
[26, [48422959787805316580, 48422959787805316581, 68480406462161287469], true]
[27, [282229692287738524679, 282229692287738524680, 399133058537705128729], true]
[28, [1644955193938625831496, 1644955193938625831497, 2326317944764069484905], true]
[29, [9587501471344016464299, 9587501471344016464300, 13558774610046711780701], true]
[30, [55880053634125472954300, 55880053634125472954301, 79026329715516201199301], true]
[31, [325692820333408821261503, 325692820333408821261504, 460599203683050495415105], true]
[32, [1898276868366327454614720, 1898276868366327454614721, 2684568892382786771291329], true]
[33, [11063968389864555906426819, 11063968389864555906426820, 15646814150613670132332869], true]
[34, [64485533470821007983946196, 64485533470821007983946197, 91196316011299234022705885], true]
[35, [375849232435061491997250359, 375849232435061491997250360, 531531081917181734003902441], true]
[36, [2190609861139547943999555960, 2190609861139547943999555961, 3097990175491791170000708761], true]
[37, [12767809934402226172000085403, 12767809934402226172000085404, 18056409971033565286000350125], true]
[38, [74416249745273809088000956460, 74416249745273809088000956461, 105240469650709600546001391989], true]
[39, [433729688537240628356005653359, 433729688537240628356005653360, 613386407933224037990008001809], true]
[40, [2527961881478169961048032963696, 2527961881478169961048032963697, 3575077977948634627394046618865], true]
[41, [14734041600331779137932192128819, 14734041600331779137932192128820, 20837081459758583726374271711381], true]
[42, [85876287720512504866545119809220, 85876287720512504866545119809221, 121447410780602867730851583649421], true]
[43, [500523684722743250061338526726503, 500523684722743250061338526726504, 707847383223858622658735230185145], true]
[44, [2917265820615946995501486040549800, 2917265820615946995501486040549801, 4125636888562548868221559797461449], true]
[45, [17003071238972938722947577716572299, 17003071238972938722947577716572300, 24045973948151434586670623554583549], true]
[46, [99101161613221685342183980258883996, 99101161613221685342183980258883997, 140150206800346058651802181530039845], true]
[47, [577603898440357173330156303836731679, 577603898440357173330156303836731680, 816855266853924917324142465625655521], true]
[48, [3366522229028921354638753842761506080, 3366522229028921354638753842761506081, 4760981394323203445293052612223893281], true]
[49, [19621529475733170954502366752732304803, 19621529475733170954502366752732304804, 27749033099085295754434173207717704165], true]
[50, [114362654625370104372375446673632322740, 114362654625370104372375446673632322741, 161733217200188571081311986634082331709], true]
[51, [666554398276487455279750313289061631639, 666554398276487455279750313289061631640, 942650270102046130733437746596776286089], true]
[52, [3884963735033554627306126433060737467096, 3884963735033554627306126433060737467097, 5494168403412088213319314492946575384825], true]
[53, [22643228011924840308557008285075363170939, 22643228011924840308557008285075363170940, 32022360150370483149182449211082676022861], true]
[54, [131974404336515487224035923277391441558540, 131974404336515487224035923277391441558541, 186639992498810810681775380773549480752341], true]
[55, [769203198007168083035658531379273286180303, 769203198007168083035658531379273286180304, 1087817594842494380941469835430214208491185], true]
[56, [4483244783706493010989915264998248275523280, 4483244783706493010989915264998248275523281, 6340265576556155474967043631807735770194769], true]
[57, [26130265504231789982903833058610216366959379, 26130265504231789982903833058610216366959380, 36953775864494438468860791955416200412677429], true]
[58, [152298348241684246886433083086663049926232996, 152298348241684246886433083086663049926232997, 215382389610410475338197708100689466705869805], true]
[59, [887659823945873691335694665461368083190438599, 887659823945873691335694665461368083190438600, 1255340561797968413560325456648720599822541401], true]
[60, [5173660595433557901127734909681545449216398600, 5173660595433557901127734909681545449216398601, 7316660981177400006023755031791634132229378601], true]
[61, [30154303748655473715430714792627904612107953003, 30154303748655473715430714792627904612107953004, 42644625325266431622582204734101084193553730205], true]
[62, [175752161896499284391456553846085882223431319420, 175752161896499284391456553846085882223431319421, 248551090970421189729469473372814871029093002629], true]
[63, [1024358667630340232633308608283887388728479963519, 1024358667630340232633308608283887388728479963520, 1448661920497260706754234635502788141981004285569], true]
[64, [5970399843885542111408395095857238450147448461696, 5970399843885542111408395095857238450147448461697, 8443420432013143050795938339643913980856932710785], true]
[65, [34798040395682912435817061966859543312156210806659, 34798040395682912435817061966859543312156210806660, 49211860671581597598021395402360695743160591979141], true]
[66, [202817842530211932503493976705300021422789816378260, 202817842530211932503493976705300021422789816378261, 286827743597476442537332434074520260478106619164061], true]
[67, [1182109014785588682585146798264940585224582687462903, 1182109014785588682585146798264940585224582687462904, 1671754600913277057625973209044760867125479123005225], true]
[68, [6889836246183320163007386812884343489924706308399160, 6889836246183320163007386812884343489924706308399161, 9743699861882185903218506820194044942274768118867289], true]
[69, [40156908462314332295459174079041120354323655162932059, 40156908462314332295459174079041120354323655162932060, 56790444570379838361685067712119508786523129590198509], true]
[70, [234051614527702673609747657661362378636017224669193196, 234051614527702673609747657661362378636017224669193197, 330998967560396844266891899452523007776864009422323765], true]
[71, [1364152778703901709363026771889133151461779692852227119, 1364152778703901709363026771889133151461779692852227120, 1929203360792001227239666329003018537874660926943744081], true]
[72, [7950865057695707582568412973673436530134660932444169520, 7950865057695707582568412973673436530134660932444169521, 11244221197191610519171106074565588219471101552240140721], true]
[73, [46341037567470343786047451070151486029346185901812790003, 46341037567470343786047451070151486029346185901812790004, 65536123822357661887786970118390510778951948386497100245], true]
[74, [270095360347126355133716293447235479645942454478432570500, 270095360347126355133716293447235479645942454478432570501, 381972521736954360807550714635777476454240588766742460749], true]
[75, [1574231124515287787016250309613261391846308540968782632999, 1574231124515287787016250309613261391846308540968782633000, 2226299006599368502957517317696274347946491584213957664249], true]
[76, [9175291386744600366963785564232332871431908791334263227496, 9175291386744600366963785564232332871431908791334263227497, 12975821517859256656937553191541868611224708916517003524745], true]
[77, [53477517195952314414766463075780735836745144207036796731979, 53477517195952314414766463075780735836745144207036796731980, 75628630100556171438667801831554937319401761914888063484221], true]
[78, [311689811788969286121634992890452082149038956450886517164380, 311689811788969286121634992890452082149038956450886517164381, 440795959085477771975069257797787755305185862572811377380581], true]
[79, [1816661353537863402315043494266931757057488594498282306254303, 1816661353537863402315043494266931757057488594498282306254304, 2569147124412310460411747744955171594511713413521980200799265], true]
[80, [10588278309438211127768625972711138460195892610538807320361440, 10588278309438211127768625972711138460195892610538807320361441, 14974086787388384990495417211933241811765094618559069827415009], true]
[81, [61713008503091403364296712341999899004117867068734561615914339, 61713008503091403364296712341999899004117867068734561615914340, 87275373599917999482560755526644279276078854297832438763690789], true]
[82, [359689772709110209058011648079288255564511309801868562375124596, 359689772709110209058011648079288255564511309801868562375124597, 508678154812119611904869115947932433844708031168435562754729725], true]
[83, [2096425627751569850983773176133729634382949991742476812634833239, 2096425627751569850983773176133729634382949991742476812634833240, 2964793555272799671946653940160950323792169332712780937764687561], true]
[84, [12218863993800308896844627408723089550733188640652992313433874840, 12218863993800308896844627408723089550733188640652992313433874841, 17280083176824678419775054525017769508908307965108250063833395641], true]
[85, [71216758335050283530083991276204807670016181852175477067968415803, 71216758335050283530083991276204807670016181852175477067968415804, 100715705505675270846703673209945666729657678457936719445235686285], true]
[86, [415081686016501392283659320248505756469363902472399870094376619980, 415081686016501392283659320248505756469363902472399870094376619981, 587014149857226946660446984734656230869037762782512066607580722069], true]
[87, [2419273357763958070171871930214829731146167232982223743498291304079, 2419273357763958070171871930214829731146167232982223743498291304080, 3421369193637686409115978235197991718484568898237135680200248646129], true]
[88, [14100558460567247028747572261040472630407639495420942590895371204496, 14100558460567247028747572261040472630407639495420942590895371204497, 19941201011968891508035422426453294080038375626640302014593911154705], true]
[89, [82184077405639524102313561636028006051299669739543431801873935922899, 82184077405639524102313561636028006051299669739543431801873935922900, 116225836878175662639096556323521772761745684861604676407363218282101], true]
[90, [479003905973269897585133797555127563677390378941839648220348244332900, 479003905973269897585133797555127563677390378941839648220348244332901, 677413820257085084326543915514677342490435733542987756429585398537901], true]
[91, [2791839358433979861408489223694737376013042603911494457520215530074503, 2791839358433979861408489223694737376013042603911494457520215530074504, 3948257084664334843320166936764542282180868716396321862170149172945305], true]
[92, [16272032244630609270865801544613296692400865244527127096900944936114120, 16272032244630609270865801544613296692400865244527127096900944936114121, 23012128687728923975594457705072576350594776564834943416591309639133929], true]
[93, [94840354109349675763786320043985042778392148863251268123885454086610219, 94840354109349675763786320043985042778392148863251268123885454086610220, 134124515041709209010246579293670915821387790672613338637377708661858269], true]
[94, [552770092411467445311852118719296959977952027934980481646411779583547196, 552770092411467445311852118719296959977952027934980481646411779583547197, 781734961562526330085885018056952918577731967470845088407674942332015685], true]
[95, [3221780200359454996107326392271796717089320018746631621754585223414672959, 3221780200359454996107326392271796717089320018746631621754585223414672960, 4556285254333448771505063529048046595645004014152457191808671945330235841], true]
[96, [18777911109745262531332106234911483342557968084544809248881099560904490560, 18777911109745262531332106234911483342557968084544809248881099560904490561, 26555976564438166298944496156231326655292292117443898062444356729649399361], true]
[97, [109445686458112120191885311017197103338258488488522223871532012142012270403, 109445686458112120191885311017197103338258488488522223871532012142012270404, 154779574132295549022161913408339913336108748690510931182857468432566160325], true]
[98, [637896207638927458619979759868271136686992962846588533980310973291169131860, 637896207638927458619979759868271136686992962846588533980310973291169131861, 902121468229335127834026984293808153361360200025621689034700453865747562589], true]
[99, [3717931559375452631527993248192429716783699288591008980010333827605002520759, 3717931559375452631527993248192429716783699288591008980010333827605002520760, 5257949235243715217981999992354509006832052451463219203025345254761919215209], true]
[100, [21669693148613788330547979729286307164015202768699465346081691992338845992696, 21669693148613788330547979729286307164015202768699465346081691992338845992697, 30645573943232956180057972969833245887630954508753693529117371074705767728665], true]

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