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2016年9月30日 (金)

ペレリマン数列(2乗するともとに戻る数)の計算をカシオの高精度計算サイトkeisan.casio.jpにUP!(加藤文元さんの天に向かって続く数より)

加藤文元さん、中井保行さん著の天に向かって続く数を読み始めています。
最初から面白いです。表紙も素敵。
で、読み進める前に(ってのも変ですが)、出てくるペレリマン数列の具体的な計算を
カシオの高精度計算サイト、keisan.casio.jpに自作式としてUP!
これです。

 

 

例えばn=10としたら、こんな感じに。n=23までは計算できます。
n Pn Qn Pn+Qn Pn*Qn
0 5 6 11 30
1 25 76 101 1,900
2 625 376 1,001 235,000
3 625 9,376 10,001 5,860,000
4 90,625 9,376 100,001 849,700,000
5 890,625 109,376 1,000,001 97,413,000,000
6 2,890,625 7,109,376 10,000,001 20,550,540,000,000
7 12,890,625 87,109,376 100,000,001 1,122,894,300,000,000
8 212,890,625 787,109,376 1,000,000,001 167,568,207,000,000,000
9 8,212,890,625 1,787,109,376 10,000,000,001 14,677,333,840,000,000,000
10 18,212,890,625 81,787,109,376 100,000,000,001 1,489,579,677,600,000,000,000

PnとQnを二乗したのはこうなる。

n Pn Qn Pn*Pn Qn*Qn
0 5 6 25 36
1 25 76 625 5776
2 625 376 390625 141376
3 625 9376 390625 87909376
4 90625 9376 8212890625 87909376
5 890625 109376 793212890625 11963109376
6 2890625 7109376 8355712890625 50543227109376
7 12890625 87109376 166168212890625 7588043387109376
8 212890625 787109376 45322418212890625 619541169787109376
9 8212890625 1787109376 67451572418212890625 3193759921787109376
10 18212890625 81787109376 331709384918212890625 6689131260081787109376


 

 

 

 


 

 

 

 


 

 

 

こちらも参照:

ペレリマン数列(2乗するともとに戻る数)を10000桁までPari/GPで計算(天に向かって続く数、加藤文元さん著)

 

※ちなみに自作式は50桁しか使えませんが、フリー計算にすると130桁まで計算できるので、n=64くらいまで計算できる。

https://keisan.casio.jp/calculator

n Pn Qn Pn+Qn Pn*Qn
0 5 6 11 30
1 25 76 101 1900
2 625 376 1001 235000
3 625 9376 10001 5860000
4 90625 9376 100001 849700000
5 890625 109376 1000001 97413000000
6 2890625 7109376 10000001 20550540000000
7 12890625 87109376 100000001 1122894300000000
8 212890625 787109376 1000000001 167568207000000000
9 8212890625 1787109376 10000000001 14677333840000000000
10 18212890625 81787109376 100000000001 1489579677600000000000
11 918212890625 81787109376 1000000000001 75097978116000000000000
12 9918212890625 81787109376 10000000000001 811181962500000000000000
13 59918212890625 40081787109376 100000000000001 2401629053056300000000000000
14 259918212890625 740081787109376 1000000000000001 192360735498369000000000000000
15 6259918212890625 3740081787109376 10000000000000001 23412606096826500000000000000000
16 56259918212890625 43740081787109376 100000000000000001 2460813423967920300000000000000000
17 256259918212890625 743740081787109376 1000000000000000001 190590772530413233000000000000000000
18 2256259918212890625 7743740081787109376 10000000000000000001 17471890363594866360000000000000000000
19 92256259918212890625 7743740081787109376 100000000000000000001 714408497724434710200000000000000000000
20 392256259918212890625 607743740081787109376 1000000000000000000001 238391286473188301898000000000000000000000
21 7392256259918212890625 2607743740081787109376 10000000000000000000001 19277109986882123848780000000000000000000000
22 77392256259918212890625 22607743740081787109376 100000000000000000000001 1749664296990971479317600000000000000000000000
23 977392256259918212890625 22607743740081787109376 1000000000000000000000001 22096633663064579877756000000000000000000000000
24 9977392256259918212890625 22607743740081787109376 10000000000000000000000001 225566327323800663862140000000000000000000000000
25 19977392256259918212890625 80022607743740081787109376 100000000000000000000000001 1598643024265518075566205900000000000000000000000000
26 619977392256259918212890625 380022607743740081787109376 1000000000000000000000000001 235605425347387542611699019000000000000000000000000000
27 6619977392256259918212890625 3380022607743740081787109376 10000000000000000000000000001 22375673248578607787973027150000000000000000000000000000
28 6619977392256259918212890625 93380022607743740081787109376 100000000000000000000000000001 618173638551642000427133183400000000000000000000000000000
29 106619977392256259918212890625 893380022607743740081787109376 1000000000000000000000000000001 95252157813131023943176156621000000000000000000000000000000
30 4106619977392256259918212890625 5893380022607743740081787109376 10000000000000000000000000000001 24201872135205387283861389047250000000000000000000000000000000
31 4106619977392256259918212890625 95893380022607743740081787109376 100000000000000000000000000000001 393797670100508450676500549203500000000000000000000000000000000
32 4106619977392256259918212890625 995893380022607743740081787109376 1000000000000000000000000000000001 4089755649753539084602892150766000000000000000000000000000000000
33 9004106619977392256259918212890625 995893380022607743740081787109376 10000000000000000000000000000000001 8967130175853223232745338976135150000000000000000000000000000000000
34 9004106619977392256259918212890625 90995893380022607743740081787109376 100000000000000000000000000000000001 819336725973818526296137978136291400000000000000000000000000000000000
35 109004106619977392256259918212890625 890995893380022607743740081787109376 1000000000000000000000000000000000001 97122211359957993105678080727159729000000000000000000000000000000000000
36 6109004106619977392256259918212890625 3890995893380022607743740081787109376 10000000000000000000000000000000000001 23770109891500025816336898326088487860000000000000000000000000000000000000
37 96109004106619977392256259918212890625 3890995893380022607743740081787109376 100000000000000000000000000000000000001 373959740295702060513273505686928331700000000000000000000000000000000000000
38 896109004106619977392256259918212890625 103890995893380022607743740081787109376 1000000000000000000000000000000000000001 93097656865661717885933891562937904895000000000000000000000000000000000000000
39 896109004106619977392256259918212890625 9103890995893380022607743740081787109376 10000000000000000000000000000000000000001 8158078693825241514416240230826853920520000000000000000000000000000000000000000
40 30896109004106619977392256259918212890625 69103890995893380022607743740081787109376 100000000000000000000000000000000000000001 2135041348817023840836183928028373240639300000000000000000000000000000000000000000
41 230896109004106619977392256259918212890625 769103890995893380022607743740081787109376 1000000000000000000000000000000000000000001 177583095850870333829532312057987479685952000000000000000000000000000000000000000000
42 3230896109004106619977392256259918212890625 6769103890995893380022607743740081787109376 10000000000000000000000000000000000000000001 21870271422863190193761709080837742118357830000000000000000000000000000000000000000000
43 23230896109004106619977392256259918212890625 76769103890995893380022607743740081787109376 100000000000000000000000000000000000000000001 1783415076873068521192631321893833652762889100000000000000000000000000000000000000000000
44 423230896109004106619977392256259918212890625 576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000001 244106504687773479183190370547519825474051952000000000000000000000000000000000000000000000
45 3423230896109004106619977392256259918212890625 6576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000001 22513799193014785799043122547316299580112723830000000000000000000000000000000000000000000000
46 23423230896109004106619977392256259918212890625 76576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000001 1793675343998464991130041992160129295490757255100000000000000000000000000000000000000000000000
47 423423230896109004106619977392256259918212890625 576576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000000001 244135998433609365401792039731385755287312046318000000000000000000000000000000000000000000000000
48 7423423230896109004106619977392256259918212890625 2576576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000000001 19127019843953064344868692152770104455696247593200000000000000000000000000000000000000000000000000
49 57423423230896109004106619977392256259918212890625 42576576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000000001 2444892787534991974303802492378847541856514118687000000000000000000000000000000000000000000000000000
50 557423423230896109004106619977392256259918212890625 442576576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000000000001 246702550464445381073893140494639621915864692829625000000000000000000000000000000000000000000000000000
51 557423423230896109004106619977392256259918212890625 9442576576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000000000001 5263513359542510362110852720291169928255128608845250000000000000000000000000000000000000000000000000000
52 557423423230896109004106619977392256259918212890625 99442576576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000000000001 55431621450323160172480448518256472991647767769001500000000000000000000000000000000000000000000000000000
53 557423423230896109004106619977392256259918212890625 999442576576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000000000000001 557112702358129658276176406497909503625574159370564000000000000000000000000000000000000000000000000000000
54 1000557423423230896109004106619977392256259918212890625 8999442576576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000000000000001 9004459076664974402421304922746339655297445001649604940000000000000000000000000000000000000000000000000000000
55 11000557423423230896109004106619977392256259918212890625 88999442576576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000000000000001 979043478716291137130051592386144757113235639276551948700000000000000000000000000000000000000000000000000000000
56 811000557423423230896109004106619977392256259918212890625 188999442576576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000000000000000001 153278653282320029509853748717752160582533853696527528512000000000000000000000000000000000000000000000000000000000
57 3811000557423423230896109004106619977392256259918212890625 6188999442576576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000000000000000001 23586280325552589722198180761037612092759302633451166200390000000000000000000000000000000000000000000000000000000000
58 63811000557423423230896109004106619977392256259918212890625 36188999442576576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000000000000000001 2309256263602849892795314910637839012770991614835904779481700000000000000000000000000000000000000000000000000000000000
59 863811000557423423230896109004106619977392256259918212890625 136188999442576576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000000000000000000001 117641555873406453631168038607763205028596412232893155756045000000000000000000000000000000000000000000000000000000000000
60 863811000557423423230896109004106619977392256259918212890625 9136188999442576576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000000000000000000001 7891940560890217262709233019644722784825126718572157071771670000000000000000000000000000000000000000000000000000000000000
61 80863811000557423423230896109004106619977392256259918212890625 19136188999442576576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000000000000000000001 1547425170521870577636546505389357259386407668780377882169428000000000000000000000000000000000000000000000000000000000000000
62 580863811000557423423230896109004106619977392256259918212890625 419136188999442576576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000000000000000000000001 243461044070466128235313456894488946597388668443154386060880366000000000000000000000000000000000000000000000000000000000000000
63 9580863811000557423423230896109004106619977392256259918212890625 419136188999442576576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000000000000000000000001 4015686745065449317426235391913451987017592138136815122144864750000000000000000000000000000000000000000000000000000000000000000
64 9580863811000557423423230896109004106619977392256259918212890625 90419136188999442576576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000000000000000000000001 866293429735115617425517016041723821582815557441200207761305021000000000000000000000000000000000000000000000000000000000000000000
65 509580863811000557423423230896109004106619977392256259918212890625 490419136188999442576576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000000000000000000000000001 2.49908207048635059875083193926430823410920817818215574215940015959E+131
66 6509580863811000557423423230896109004106619977392256259918212890625 3490419136188999442576576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000000000000000000000000001 2.272116561561563338760481350123810381109106088564144679446130134409E+133
67 66509580863811000557423423230896109004106619977392256259918212890625 33490419136188999442576576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000000000000000000000000001 2.2274337397012856166649021165743548336878924615638737589969149146254E+135
68 166509580863811000557423423230896109004106619977392256259918212890625 833490419136188999442576576769103890995893380022607743740081787109376 1000000000000000000000000000000000000000000000000000000000000000000001 1.38784140344368986006861298378201631136562526445738453140939663938063E+137
69 2166509580863811000557423423230896109004106619977392256259918212890625 7833490419136188999442576576769103890995893380022607743740081787109376 10000000000000000000000000000000000000000000000000000000000000000000001 1.697133204466342398879397841453268217615709562633269973444053072839119E+139
70 62166509580863811000557423423230896109004106619977392256259918212890625 37833490419136188999442576576769103890995893380022607743740081787109376 100000000000000000000000000000000000000000000000000000000000000000000001 2.3519760446187490939720712757176057989060338970270109320466429843416725E+141

 

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