コラッツ数列を逆向きに考察
コラッツ数列を逆向きに考察
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「コラッツ予想」
奇数偶数の連続サイクルについて考察
コラッツ数列を逆向きに考察
奇数Ａを起点に２倍を無限に適応した数列を奇数Ａの倍数列と名付ける
奇数Ａの倍数列は
Ａ≡０（ｍｏｄ３） では分岐は起こらない
Ａ≡１（ｍｏｄ３） では４倍毎に分岐する
Ａ≡２（ｍｏｄ３） では2倍から分岐が始まりその後は４倍毎に分岐する
奇数Ａの倍数列から4倍毎に分岐する奇数Ｃは3回に1回は必ず３の倍数になる
３の倍数の奇数Ａの倍数列は分岐しないので他の奇数からの接続もない故に
３の倍数の奇数Ａ及び倍数列はコラッツ数列の先頭のみにしか存在できない
分岐した奇数Ｃ１は分岐順に次の奇数Ｃ２とＣ２＝Ｃ１×４＋１の関係が成り立つ
1<2<4<8<16<32<64<128<256<512<1024<2048<4096<8192<16384<32768<65536<131072<262144....
1 5 21≡0 85 341 1365≡0 5461 21845 87381≡0
| | | | | --<43690<87380<....
| | | | | 14563<29126<58252....
| | | | | 19417<38834<....
| | | | --<10922<21844<43688<87376<174752<....
| | | | 7281≡0 29125<58250<....
| | | --<2730<5460<10920<21840<43680......≡0
| | --<682<1364<2728<5456<10912<21824<43648<87296<174592<.....
| | 227 909≡0 3637 14549 58197≡0
| | | | --<29098<58196<116392<....
| | | | 9699≡0 38797<77594<....
| | | --<7274<14548<29096<58192<116384<....
| | | 4849 19397<38794<....
| | | | 12931<25862<....
| | | --<9698<19396<38792<77584<.....
| | | 6465≡0 25861<.....
| | --<454<908<1816<3632<7264<14528<29056<58112<116224<.....
| | 151 605 2421≡0 9685 38741<.....
| | | --<1210<2420<..... --<19370<38740<.....
| | | 403<806<1612<3224<6448<12896<.....
| | | 537≡0 2149<4298<......
| | --<302<604<1208<2416<4832<9664<19328<38656<....
| | 201≡0 805 3221 12885≡0
| | | --<6442<12884<....
| | | 2147<4294<....
| | | 1431<....
| | --<1610<3220<6440<12880<....
| | 1073 4293≡0
| | --<2146<4292<8584<....
| | 715 2861<....
| | --<1430<2860<....
| | 953<1906<....
| | 635<....
| --<170<340<680<1360<2720<5440<10880<21760<43520<87040<......
| 113 453≡0 1813 7253 29013≡0
| | | --<14506<29012<58024<.....
| | | 4835 19341≡0
| | | --<9670<19340<38680<.....
| | | 3223 12893<25786<.....
| | | | 8595≡0
| | | --<6446<12892<25784<.....
| | | 4297<8594<17188<.....
| | | 5729<.....
| | --<3626<7252<14504<29008<58016<116032<.....
| | 2417 9669≡0 38677<.....
| | --<4834<9668<19336<38672<77344<.....
| | 1611≡0 6445 25781<.....
| | --<12890<25780<.....
| --<226<452<904<1808<3616<7232<..... 8593<.....
| 75≡0 301 1205<2410<4820<9640<19280<38560<.....
| | 803 3213≡0 12853<.....
| | --<1606<3212<6424<12848<.....
| | 535 2141<4282<.....
| | | 1427<.....
| | --<1070<2140<4280<.....
| | 713<1426<.....
| | 475<.....
| --<602<1204<2408<4816<9632<19264<38528<....
| 401 1605≡0 6421<12842<....
| --<802<1604<3208<6416<12832<25664<....
| 267≡0 1069 4277<8554<.....
| | 2851<.....
| --<2138<4276<8552<17104<....
| 1425≡0 5701<....
--<10<20<40<80<160<320<640<1280<2560<5120<10240<20480<40960<81920<163840<....
3≡0 13 53 213≡0 853 3413 13653≡0 54613<109226<....
| | | --<6826<13652<27304<54608<109216<....
| | | 2275 9101 36405≡0
| | | | --<18202<36404<.....
| | | | 6067<12134<.....
| | | --<4550<9100<18200<36400<....
| | | 3033≡0 12133<....
| | -<1706<3412<6824<13648<27296<54592<....
| | 1137≡0 4549 18197<....
| | --<9098<18196<36392<.....
| | 6065<12130<.....
| | 4043<.....
| --<106<212<424<848<1696<3392<6784<13568<27136<54272<.....
| 35 141≡0 565 2261 9045≡0
| | | --<4522<9044<18088<36176<....
| | | 1507 6029<12058<....
| | | | 4019<....
| | | --<3014<6028<12056<....
| | | 2009<4018<....
| | | 1339<....
| | --<1130<2260<4520<9040<18080<36160<....
| | 753≡0 3013 12053<....
| | --<6026<12052<....
| | 4017≡0
| --<70<140<280<560<1120<2240<4480<8960<17920<....
| 23 93≡0 373 1493 5973≡0
| | | --<2986<5972<11944<....
| | | 995 3981≡0
| | | --<1990<3980<....
| | | 663≡0
| | --<746<1492<2984<5968<11936<....
| | 497 1989≡0
| | --<994<1988<3976<7952<....
| | 331 1325<2650<....
| | | 883<....
| | --<662<1324<2648<5296<....
| | 441≡0 1765<....
| --<46<92<184<368<736<1472<2944<5888<11776<23552<....
| 15≡0 61 245 981≡0 3925<7850<....
| | --<490<980<1960<3920<7840<....
| | 163 653 2613≡0
| | | --<1306<2612<....
| | | 435≡0
| | --<326<652<1304<2608<5216<....
| | 217 869<1748<....
| | --<434<868<1736<3472<....
| | 289 1157<....
| | --<578<1156<....
| | 385<....
| --<122<244<488<976<1952<3904<7808<....
| 81≡0 325 1301<2602<....
| --<650<1300<2600<....
| 433<866<1732<....
| 577<....
--<26<52<104<208<416<832<1664<3328<6656<13312<26624<53248<....
17 69≡0 277 1109 4437≡0 17749<....
| | --<2218<4436<8872<17744<35488<....
| | 739 2957 11829≡0
| | | --<5914<11828<....
| | | 1971≡0
| | --<1478<2956<5912<11824<....
| | 985 3941<....
| | --<1970<3940<....
| | 1313<....
| --<554<1108<2216<4432<8864<17728<35456<....
| 369≡0 1477 5909<11918<....
| --<2954<5908<11816<....
| 1969<3938<....
--<34<68<136<272<544<1088<2176<4352<8704<17408<34816<....
11 45≡0 181 725 2901≡0 11605<....
| | --<1450<2900<5800<11600<....
| | 483≡0 1933<3866<....
| --<362<724<1448<2896<5792<11584<23168<....
| 241 965 3861≡0
| | --<1930<3860<7720<....
| | 643 2573<....
| | --<1286<2572<....
| | 857<1714<...,
| --<482<964<1928<3856<7712<....
| 321≡0 1285<2570<....
--<22<44<88<176<352<704<1408<2816<5632<11264<22528<....
7 29 117≡0 469 1877 7509≡0
| | | --<3754<7508<15016<....
| | | 1251≡0 5005<....
| | --<938<1876<3752<7504<15008<....
| | 625 2501<5002<....
| | | 1667<....
| | --<1250<2500<5000<10000<....
| | 833 3333≡0
| | --<1666<3332<6664<....
| | 555≡0 2221<....
| --<58<116<232<464<928<1856<3712<7424<14848<....
| 19 77 309≡0 1237 4949<....
| | | --<2474<4948<9896<....
| | | 1649<3298<....
| | | 1099<....
| | --<154<308<616<1232<2464<4928<9856<....
| | 51≡0 205 821 3285≡0
| | | --<1642<3284<....
| | | 547<1094<....
| | --<410<820<1640<3280<....
| | 273≡0 1093<....
| --<38<76<152<304<608<1216<2432<4864<9728<....
| 25 101 405≡0 1621<3242<....
| | --<202<404<808<1616<3232<....
| | 67 269 1077≡0
| | | --<538<1076<2152<....
| | | 179 717≡0
| | | --<358<716<....
| | | 119<238<....
| | | 79<....
| | --<134<268<536<1072<....
| | 89 357≡0
| | --<178<356<712<....
| | 237 ≡0
| --<50<100<200<400<800<1600<3200<....
| 33≡0 133 533
| | --<1066<2132<....
| | 355<710<....
| --<266<532<1064<2128<....
| 177≡0 709<....
--<14<28<56<112<224<448<896<1792<3584<7168<14336<....
9≡0 37 149 597≡0 2389<4778<....
| --<298<596<1192<2384<4768<....
| 99≡0 397 1589<3178<....
| --<794<1588<3176<....
| 529<1058<....
--<74<148<296<592<1184<2368<4736<9472<....
49 197 789≡0 3157<....
| --<394<788<1576<3152<....
| 131 525≡0
| --<262<524<1048<2096<....
| 87≡0 349<698<....
--<98<196<392<784<1568<3136<....
65 261≡0 1045<....
--<130<260<520<1040<2080<....
43 173 693≡0
| --<346<692<1384<....
| 115 461<....
| --<230<460<920<....
| 153≡0
--<86<172<344<688<1376<....
57≡0 229<458<916<....
305<....
コラッツ数列の逆数列を考えると
奇数から始まるもっとも簡単なものは2倍を無限に適応した
数列でこれを奇数Ａの倍数列と名付ける
もし倍数列内のある偶数Ｂが１を引いて３で割り切れる整数なら
分岐する事ができる、これを偶数Ｂを３で割った余りについて考えると
合同式では
Ｂ≡０（ｍｏｄ３）Ｂ×Ｎ≡０ 何倍しても０なので倍数列では分岐は永遠に起きないと言える
Ｂ≡１（ｍｏｄ３）Ｂ×４≡１ 倍々ごとに分岐すると言える
Ｂ≡２（ｍｏｄ３）Ｂ×２≡１ 倍すると分岐しそこから倍々ごとに分岐すると言える
なのでＮが１か２の場合は倍々ごとに分岐し０の時は分岐はしないと言える
まとめると奇数Ａの倍数列は
Ａ≡０（ｍｏｄ３） では分岐は起こらない
Ａ≡１（ｍｏｄ３） では４倍毎に分岐する
Ａ≡２（ｍｏｄ３） では2倍から分岐が始まりそこから４倍毎に分岐する
分岐した奇数ＣはＢの３×Ｋ＋１を１を引いて３でわるのでＫとなり
4倍した時のＣはＢの３×（Ｋ×４+１）＋１から１を引いて３で割るのでＫ×４+１となり
なので4倍毎の
Ｃは分岐順にＣ×４＋１の関係が成り立つ
Ｃ１＝Ｋから４倍ではＣ２＝Ｋ×４+１そこから４倍ではＣ３＝（Ｋ×４+１）×４＋１＝Ｋ×１６＋５
合同式では
Ｋ≡０（ｍｏｄ３）Ｋ×４+１≡１ Ｋ×１６＋５≡２
Ｋ≡１（ｍｏｄ３）Ｋ×４+１≡２ Ｋ×１６＋５≡０
Ｋ≡２（ｍｏｄ３）Ｋ×４+１≡０ Ｋ×１６＋５≡１
なのでＣ１、Ｃ２、Ｃ３のどれかは必ず３の倍数になる
故に奇数Ａを起点とする倍数列から4倍毎に分岐する奇数Ｃは3回に1回は必ず３の倍数になる
奇数Ａの倍数列から分岐するＣ１からＣ１７までを計算
[:1=b:a+1-a%2=a:b*2+(a%3)%2=d:1=j:q(d-1):j(j*2):1=i:q(b):i(i*4):b+0=b:a/3*j+(i-1)/3=e:v(e)*3+1=f:y(lf):y(?(a%3,e,0)):q(16*?(a%3)):y(e(e*4+1)):]:y
系統＿Ａ ＝ 奇数Ａの倍数列から分岐する奇数Ｃ１からＣ１７までを計算
1 =1,5,21,85,341,1365,5461,21845,87381,349525,1398101,5592405,22369621,89478485
,357913941,1431655765,5726623061
1_5 =3,13,53,213,853,3413,13653,54613,218453,873813,3495253,13981013,55924053,223696213
,894784853,3579139413,14316557653
1_21 =0
1_85 =113,453,1813,7253,29013,116053,464213,1856853,7427413,29709653,118838613,475354453
,1901417813,7605671253,30422685013,121690740053,486762960213
1_341 =227,909,3637,14549,58197,232789,931157,3724629,14898517,59594069,238376277,953505109
,3814020437,15256081749,61024326997,244097307989,976389231957
1_1365 =0
1_5461 =7281,29125,116501,466005,1864021,7456085,29824341,119297365,477189461,1908757845
,7635031381,30540125525,122160502101,488642008405
,1954568033621,7818272134485,31273088537941
1_21845 =14563,58253,233013,932053,3728213,14912853,59651413,238605653,954422613,3817690453
,15270761813,61083047253,244332189013,977328756053,3909315024213
,15637260096853,62549040387413
1_87381 =0
1_349525 =466033,1864133,7456533,29826133,119304533,477218133,1908872533,7635490133
,30541960533,122167842133,488671368533,1954685474133,7818741896533
,31274967586133,125099870344533,500399481378133,2001597925512533
1_5_3 =0
1_5_13 =17,69,277,1109,4437,17749,70997,283989,1135957,4543829,18175317,72701269,290805077
,1163220309,4652881237,18611524949,74446099797
1_5_53 =35,141,565,2261,9045,36181,144725,578901,2315605,9262421,37049685,148198741
,592794965,2371179861,9484719445,37938877781,151755511125
1_5_213 =0
1_5_853 =1137,4549,18197,72789,291157,1164629,4658517,18634069,74536277,298145109,1192580437
,4770321749,19081286997,76325147989,305300591957,1221202367829,4884809471317
1_5_3413 =2275,9101,36405,145621,582485,2329941,9319765,37279061,149116245,596464981,2385859925
,9543439701,38173758805,152695035221,610780140885,2443120563541,9772482254165
1_5_13653 =0
1_5_54613 =72817,291269,1165077,4660309,18641237,74564949,298259797,1193039189,4772156757
,19088627029,76354508117,305418032469,1221672129877,4886688519509
,19546754078037,78187016312149,312748065248597
1_85_113 =75,301,1205,4821,19285,77141,308565,1234261,4937045,19748181,78992725,315970901
,1263883605,5055534421,20222137685,80888550741,323554202965
1_85_453 =0
1_85_1813 =2417,9669,38677,154709,618837,2475349,9901397,39605589,158422357,633689429,2534757717
,10139030869,40556123477,162224493909,648897975637,2595591902549,10382367610197
1_85_7253 =4835,19341,77365,309461,1237845,4951381,19805525,79222101,316888405,1267553621
,5070214485,20280857941,81123431765,324493727061
,1297974908245,5191899632981,20767598531925
1_85_29013 =0
1_85_116053 =154737,618949,2475797,9903189,39612757,158451029,633804117,2535216469,10140865877
,40563463509,162253854037,649015416149,2596061664597,10384246658389
,41536986633557,166147946534229,664591786136917
1_85_464213 =309475,1237901,4951605,19806421,79225685,316902741,1267610965,5070443861,20281775445
,81127101781,324508407125,1298033628501,5192134514005,20768538056021
,83074152224085,332296608896341,1329186435585365
1_85_1856853 =0
1_85_7427413 =9903217,39612869,158451477,633805909,2535223637,10140894549,40563578197,162254312789
,649017251157,2596069004629,10384276018517,41537104074069,166148416296277
,664593665185109,2658374660740437,10633498642961749,42533994571846997
1_341_227 =151,605,2421,9685,38741,154965,619861,2479445,9917781,39671125,158684501,634738005
,2538952021,10155808085,40623232341,162492929365,649971717461
1_341_909 =0
1_341_3637 =4849,19397,77589,310357,1241429,4965717,19862869,79451477,317805909,1271223637
,5084894549,20339578197,81358312789,325433251157
,1301733004629,5206932018517,20827728074069
1_341_14549 =9699,38797,155189,620757,2483029,9932117,39728469,158913877,635655509,2542622037
,10170488149,40681952597,162727810389,650911241557
,2603644966229,10414579864917,41658319459669
1_341_58197 =0
1_341_232789 =310385,1241541,4966165,19864661,79458645,317834581,1271338325,5085353301,20341413205
,81365652821,325462611285,1301850445141,5207401780565,20829607122261
,83318428489045,333273713956181,1333094855824725
1_341_931157 =620771,2483085,9932341,39729365,158917461,635669845,2542679381,10170717525,40682870101
,162731480405,650925921621,2603703686485,10414814745941,41659258983765
,166637035935061,666548143740245,2666192574960981
1_341_3724629 =0
1_341_14898517 =19864689,79458757,317835029,1271340117,5085360469,20341441877,81365767509,325463070037
,1301852280149,5207409120597,20829636482389,83318545929557,333274183718229
,1333096734872917,5332386939491669,21329547757966677,85318191031866709
1_5461_7281 =0
1_5461_29125 =38833,155333,621333,2485333,9941333,39765333,159061333,636245333,2544981333
,10179925333,40719701333,162878805333,651515221333,2606060885333
,10424243541333,41696974165333,166787896661333
1_5461_116501 =77667,310669,1242677,4970709,19882837,79531349,318125397,1272501589,5090006357
,20360025429,81440101717,325760406869,1303041627477,5212166509909
,20848666039637,83394664158549,33357865663419
1_5461_466005 =0
1_5461_1864021 =2485361,9941445,39765781,159063125,636252501,2545010005,10180040021,40720160085
,162880640341,651522561365,2606090245461,10424360981845,41697443927381
,166789775709525,667159102838101,2668636411352405,10674545645409621
1_5461_7456085 =4970723,19882893,79531573,318126293,1272505173,5090020693,20360082773,81440331093
,325761324373,1303045297493,5212181189973,20848724759893,83394899039573
,333579596158293,1334318384633173,5337273538532693,21349094154130773
1_5461_29824341 =0
1_5461_119297365 =159063153,636252613,2545010453,10180041813,40720167253,162880669013,651522676053
,2606090704213,10424362816853,41697451267413,166789805069653,667159220278613
,2668636881114453,10674547524457813,42698190097831253,170792760391325013
,683171041565300053
1_5461_477189461 =318126307,1272505229,5090020917,20360083669,81440334677,325761338709,1303045354837
,5212181419349,20848725677397,83394902709589,333579610838357,1334318443353429
,5337273773413717,21349095093654869,85396380374619477,341585521498477909
,1366342085993911637
1_21845_14563 =19417,77669,310677,1242709,4970837,19883349,79533397,318133589,1272534357
,5090137429,20360549717,81442198869,325768795477,1303075181909
,5212300727637,20849202910549,83396811642197
1_21845_58253 =38835,155341,621365,2485461,9941845,39767381,159069525,636278101,2545112405
,10180449621,40721798485,162887193941,651548775765,2606195103061
,10424780412245,41699121648981,166796486595925
1_21845_233013 =0
1_21845_932053 =1242737,4970949,19883797,79535189,318140757,1272563029,5090252117,20361008469
,81444033877,325776135509,1303104542037,5212418168149,20849672672597
,83398690690389,333594762761557,1334379051046229,5337516204184917
1_21845_3728213 =2485475,9941901,39767605,159070421,636281685,2545126741,10180506965,40722027861
,162888111445,651552445781,2606209783125,10424839132501,41699356530005
,166797426120021,667189704480085,2668758817920341,10675035271681365
1_21845_14912853 =0
1_21845_59651413 =79535217,318140869,1272563477,5090253909,20361015637,81444062549,325776250197
,1303105000789,5212420003157,20849680012629,83398720050517,333594880202069
,1334379520808277,5337518083233109,21350072332932437,85400289331729749
,341601157326918997
1_21845_238605653 =159070435,636281741,2545126965,10180507861,40722031445,162888125781,651552503125
,2606210012501,10424840050005,41699360200021,166797440800085,667189763200341
,2668759052801365,10675036211205461,42700144844821845,170800579379287381
,683202317517149525
1_21845_954422613 =0
1_349525_466033 =621377,2485509,9942037,39768149,159072597,636290389,2545161557,10180646229
,40722584917,162890339669,651561358677,2606245434709,10424981738837
,41699926955349,166799707821397,667198831285589,2668795325142357
1_349525_1864133 =1242755,4971021,19884085,79536341,318145365,1272581461,5090325845,20361303381
,81445213525,325780854101,1303123416405,5212493665621,20849974662485
,83399898649941,333599594599765,1334398378399061,5337593513596245
1_349525_7456533 =0
1_349525_29826133 =39768177,159072709,636290837,2545163349,10180653397,40722613589,162890454357
,651561817429,2606247269717,10424989078869,41699956315477,166799825261909
,667199301047637,2668797204190549,10675188816762197,42700755267048789
,170803021068195157
1_349525_119304533 =79536355,318145421,1272581685,5090326741,20361306965,81445227861,325780911445
,1303123645781,5212494583125,20849978332501,83399913330005,333599653320021
,1334398613280085,5337594453120341,21350377812481365,85401511249925461
,341606044999701845
1_349525_477218133 =0
1_349525_1908872533 =2545163377,10180653509,40722614037,162890456149,651561824597,2606247298389
,10424989193557,41699956774229,166799827096917,667199308387669,2668797233550677
,10675188934202709,42700755736810837,170803022947243349,683212091788973397
,2732848367155893589,10931393468623574357
1_349525_7635490133 =5090326755,20361307021,81445228085,325780912341,1303123649365,5212494597461
,20849978389845,83399913559381,333599654237525,1334398616950101,5337594467800405
,21350377871201621,85401511484806485,341606045939225941,1366424183756903765
,5465696735027615061,21862786940110460245
1_349525_30541960533 =0
1_5_13_17 =11,45,181,725,2901,11605,46421,185685,742741,2970965,11883861,47535445,190141781
,760567125,3042268501,12169074005,48676296021
1_5_13_69 =0
1_5_13_277 =369,1477,5909,23637,94549,378197,1512789,6051157,24204629,96818517,387274069
,1549096277,6196385109,24785540437,99142161749,396568646997,1586274587989
1_5_13_1109 =739,2957,11829,47317,189269,757077,3028309,12113237,48452949,193811797,775247189
,3100988757,12403955029,49615820117,198463280469,793853121877,3175412487509
1_5_13_4437 =0
1_5_13_ 17749 =23665,94661,378645,1514581,6058325,24233301,96933205,387732821,1550931285
,6203725141,24814900565,99259602261,397038409045,1588153636181
,6352614544725,25410458178901,101641832715605
1_5_13_70997 =47331,189325,757301,3029205,12116821,48467285,193869141,775476565,3101906261
,12407625045,49630500181,198522000725,794088002901,3176352011605
,12705408046421,50821632185685,203286528742741
1_5_13_283989 =0
1_5_13_1135957 =1514609,6058437,24233749,96934997,387739989,1550959957,6203839829,24815359317
,99261437269,397045749077,1588182996309,6352731985237,25410927940949
,101643711763797,406574847055189,1626299388220757,6505197552883029
1_5_53_35 =23,93,373,1493,5973,23893,95573,382293,1529173,6116693,24466773,97867093
,391468373,1565873493,6263493973,25053975893,100215903573
1_5_53_141 =0
1_5_53_565 =753,3013,12053,48213,192853,771413,3085653,12342613,49370453,197481813,789927253
,3159709013,12638836053,50555344213,202221376853,808885507413,3235542029653
1_5_53_2261 =1507,6029,24117,96469,385877,1543509,6174037,24696149,98784597,395138389
,1580553557,6322214229,25288856917,101155427669,404621710677
,1618486842709,6473947370837
1_5_53_9045 =0
1_5_53_36181 =48241,192965,771861,3087445,12349781,49399125,197596501,790386005,3161544021
,12646176085,50584704341,202338817365,809355269461,3237421077845
,12949684311381,51798737245525,207194948982101
1_5_53_144725 =96483,385933,1543733,6174933,24699733,98798933,395195733,1580782933,6323131733
,25292526933,101170107733,404680430933,1618721723733,6474886894933
,25899547579733,103598190318933,414392761275733
1_5_53_578901 =0
1_5_53_2315605 =3087473,12349893,49399573,197598293,790393173,3161572693,12646290773,50585163093
,202340652373,809362609493,3237450437973,12949801751893,51799207007573
,207196828030293,828787312121173,3315149248484693,13260596993938773
1_5_853_1137 =0
1_5_853_4549 =6065,24261,97045,388181,1552725,6210901,24843605,99374421,397497685,1589990741
,6359962965,25439851861,101759407445,407037629781,1628150519125,6512602076501
,26050408306005
1_5_853_18197 =12131,48525,194101,776405,3105621,12422485,49689941,198759765,795039061
,3180156245,12720624981,50882499925,203529999701,814119998805
,3256479995221,13025919980885,52103679923541
1_5_853_72789 =0
1_5_853_291157 =388209,1552837,6211349,24845397,99381589,397526357,1590105429,6360421717
,25441686869,101766747477,407066989909,1628267959637,6513071838549
,26052287354197,104209149416789,416836597667157,1667346390668629
1_5_853_1164629 =776419,3105677,12422709,49690837,198763349,795053397,3180213589,12720854357
,50883417429,203533669717,814134678869,3256538715477,13026154861909
,52104619447637,208418477790549,833673911162197,3334695644648789
1_5_853_4658517 =0
1_5_853_18634069 =24845425,99381701,397526805,1590107221,6360428885,25441715541,101766862165
,407067448661,1628269794645,6513079178581,26052316714325,104209266857301
,416837067429205,1667348269716821,6669393078867285,26677572315469141
,106710289261876565
1_5_853_74536277 =49690851,198763405,795053621,3180214485,12720857941,50883431765,203533727061
,814134908245,3256539632981,13026158531925,52104634127701,208418536510805
,833674146043221,3334696584172885,13338786336691541,53355145346766165
,213420581387064661
1_5_3413_2275 =3033,12133,48533,194133,776533,3106133,12424533,49698133,198792533
,795170133,3180680533,12722722133,50890888533,203563554133
,814254216533,3257016866133,13028067464533
1_5_3413_9101 =6067,24269,97077,388309,1553237,6212949,24851797,99407189,397628757
,1590515029,6362060117,25448240469,101792961877,407171847509
,1628687390037,6514749560149,26058998240597
1_5_3413_36405 =0
1_5_3413_145621 =194161,776645,3106581,12426325,49705301,198821205,795284821,3181139285
,12724557141,50898228565,203592914261,814371657045,3257486628181
,13029946512725,52119786050901,208479144203605,833916576814421
1_5_3413_582485 =388323,1553293,6213173,24852693,99410773,397643093,1590572373,6362289493
,25449157973,101796631893,407186527573,1628746110293,6514984441173
,26059937764693,104239751058773,416959004235093,1667836016940373
1_5_3413_2329941 =0
1_5_3413_9319765 =12426353,49705413,198821653,795286613,3181146453,12724585813,50898343253
,203593373013,814373492053,3257493968213,13029975872853,52119903491413
,208479613965653,833918455862613,3335673823450453,13342695293801813
,53370781175207253
1_5_3413_37279061 =24852707,99410829,397643317,1590573269,6362293077,25449172309,101796689237
,407186756949,1628747027797,6514988111189,26059952444757,104239809779029
,416959239116117,1667836956464469,6671347825857877,26685391303431509
,106741565213726037
1_5_3413_149116245 =0
1_5_54613_72817 =97089,388357,1553429,6213717,24854869,99419477,397677909,1590711637
,6362846549,25451386197,101805544789,407222179157,1628888716629
,6515554866517,26062219466069,104248877864277,416995511457109
1_5_54613_291269 =194179,776717,3106869,12427477,49709909,198839637,795358549,3181434197
,12725736789,50902947157,203611788629,814447154517,3257788618069
,13031154472277,52124617889109,208498471556437,833993886225749
1_5_54613_1165077 =0
1_5_54613_4660309 =6213745,24854981,99419925,397679701,1590718805,6362875221,25451500885
,101806003541,407224014165,1628896056661,6515584226645,26062336906581
,104249347626325,416997390505301,1667989562021205,6671958248084821
,26687832992339285
1_5_54613_18641237 =12427491,49709965,198839861,795359445,3181437781,12725751125,50903004501
,203612018005,814448072021,3257792288085,13031169152341,52124676609365
,208498706437461,833994825749845,3335979302999381,13343917211997525
,53375668847990101
1_5_54613_74564949 =0
1_5_54613_298259797 =397679729,1590718917,6362875669,25451502677,101806010709,407224042837
,1628896171349,6515584685397,26062338741589,104249354966357,416997419865429
,1667989679461717,6671958717846869,26687834871387477,106751339485549909
,427005357942199637,1708021431768798549
1_5_54613_1193039189 =795359459,3181437837,12725751349,50903005397,203612021589,814448086357
,3257792345429,13031169381717,52124677526869,208498710107477,833994840429909
,3335979361719637,13343917446878549,53375669787514197,213502679150056789
,854010716600227157,3416042866400908629
1_5_54613_4772156757 =0
「コラッツ予想」
大整数電卓ツールを使ってみてください