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Digits of π in π^2 (Posted on 2023-04-27) Difficulty: 3 of 5
Where in the decimal representation of π^2 do the first N digits of π appear?

When I say "the first N digits of π", I mean counting the integer 3 but not counting the decimal point. For example, the first 5 digits of π are 31415.

Define the function pp2(N) as the N-th digit of π^2 where the first N digits of π are seen for the first time (after the decimal point).

So, pp2(1) = 13, because π^2 is approximately 9.869604401089358 and the first digit of pi, '3', first appears as the 13th digit after the decimal point.

Please find pp2(N) for N = 2,3,4,5.

  Submitted by Larry    
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Solution: (Hide)
pp2(1) = 13
pp2(2) = 37
pp2(3) = 114
pp2(4) = 7008
pp2(5) = 7008

π^2 to 8000 digits
9.8696044010893586188344909998761511353136994072407906264133493762
20044822419205243001773403718552231824025913774023144077772348122
03004672761061767798519766099039985620657563057150604123284032878
08693527693421649396665715190445387352617794138202582605816934125
15592048309818873270033076266671104358950871504100325788536595276
35775283792268331874508640454635412502697372956695833422785815000
63652270954724908597560726692647527790052853364522066698082641589
68771057327889291746901545510069254432457036449656172537928607606
00814597258922923241424004429598136181441370677777819473965830317
08566327895707534079917145231589263721144638282644328528037928503
48095233899503968574609485346009017742932205799035917357820465758
04193168682300219614689927042061429696346600579984035164213654304
99845337217365572404636768488762615122990270599380102994468861817
16260980130876530037060158369198676286005079936468322669731568367
17555897119875297529639491631553944919548387706872113078986657559
09865363656307636308806115008353739182611017808879024933772955782
16579415247442933804078677407591709391197967430171019701193399478
20225514763702291608023563586891569495798103517251511582863872932
77492004738462303294161944944950482112274446835725813185686259164
94353763920024500315482187204189247643443645633734136487845294512
75916372007430261365186821171330460897778485724432564263330723650
45231672315616051773692148498509071244808367251079619884021248924
51401396531476344595771764744875906954630437531735306768143584751
56885094684296550509413119660997619939285935287706166906809691580
20553597781851324066690861770052217484091351102484588263306531907
44031980200668972860975418524501623204699029430643716713312824652
74414551284821977475194425229367548744153531180011813932543346383
07722867084758425378966015720137099654767906621280174009756998567
04443725055207780496563411708142905142943795677474924752149438242
72325118028762798056213932631091278725616353609424784529478717542
51615265191330283407473028263587424337973810856876863949300992557
23720490122698076952839750216812862138570811782417910988340139751
81320464118845555848113002064968192010305736986644162318705215025
51644845016434425822921150995221122676823169859477070880760028354
21495127026066787989083170525169803714975503207554673935379066499
12752862709043513434577165074731682108160117628049484515765946359
41758812614520495389456565236901499040341581369495434370994611114
77011418033705087501429944601133969410999684285834770364345758834
92860123122508722027317575141993347336265838892297484958561938888
34239544151667502218841230922834931531503775433323872764004739676
71907916524882411512190035978197605342369417152590635189326325811
03657571549873169657904226714978218212845311610809607600236640118
27060294290645986837706910492665967709726606634015487578207063844
61878305752277479854412484826969160001428803019711478693597344788
59974156398142016846681818824538281428455152716656343381546134882
69646125634010584242331806504888119459980651714678470201077451172
77944162020315035637852927258377267062562705280072611694658628454
11567549279224073821787438996399441592985383492432402648218794405
97603535529046967850494820470624984189963921518775371814632179244
11189732335283988604825846749626069626284848011774145342814933313
55641534260501936653921123840517030681068214842509140354288654340
01067320722503552390254325516377456702947138170075412331140584055
90453105423509164770143749515764115646910411689551922199259124412
50635379491574344771879760729850398929956072621825781514960115469
09949578789545156511095639499194568048477769601461169809150924199
24190652202533970185704132006070922867657069381824946432719104145
61208753941841727724143921102678011284560031239056343129168023344
61082596817610850472185984702471200309971671192940623139270921696
03593028026954967153934726568438633869599464524099447180469850807
96957772595216772821201922698617876538120108971718760289683436680
25142519223060489946243443954825503928003122061817520882009392142
31089462151221142380748057529627621709580065957213615992288481309
54335580084091254724761322908812053970150240918032451541480161325
34541725485713796739568584903674764429535993311300473635976666216
08438117167562827048813989331540086932356462713340693074341619995
57602509177116455999565510797911243897900501543835083535034090126
53757497459442025015614536124068511932237930722224390121306235462
14933153525080674235949869002777468310824713671390086261683883202
59138042924795254241850385987379356756320479115800614463271069456
53496434004629296041565703410921150180388713090151481484456257860
29843376851154528924551238142190864763622635781966126001325671783
29040355012124291888102234433061447908310474373221741685334056717
49501512322346857491187209961786713844922691096325621722834656032
81153577183325350587266265301147732042003251094803695884121879153
81398685714411633626600420196345085635197044332125025771105225855
51558587825701537326327953694001760140392522666190496071808022741
63184330699021464906027452039767504013556319455527877556594434840
48103117174933359762068944341230085827169189371885821507616987358
54801584605757588122686593591270603979782687256675034141898862749
85966130902678105259900735628763665183315039575781486313060692967
60422513101592973016854108936219157943850434600990317258946423799
51900071193600960700189047527767130723855875587594980435537140931
55831489114416875297965992460526866428647633182925884899219410093
23728127012691031321923225335797771181841546904222260254856622426
42594901587020729350928495181373695709237647044325946794269231525
19168459455156899033779754083035836101640994080548216159559429867
38227049332041435359579010900202221290036779676998963640432939809
26913358336989329718916743077667797680410377730715003105378193079
55603122637174193159534957693259816217627074764094745583321835990
52611844912841942966796905963629837182698807766780115309180981462
17543091543352017427952306834517444813423217623555885825270426898
63415120325233190881979557946033919604301799108674600586109686649
30009343326241913928326439222555304992053541913132358453008186694
78029806126392202530272431058224244860709165972161313820278169580
75310151008573864217331314200774683622213231067703016805202532295
78476008633754245401930771168391695564692206163362168679728577492
08617582790814920657902305527938111963666671857886255954946278286
07515475304126278174327961367499113436260864479177769930431224298
00644734598965804677241599635867487228442130409075176687705519242
73526221983098292641175818137693773764400674411776739196946345386
39833503101871227394555068196858892459492640207369411611793113522
85694151355423685081115422986845476691718066932921230690860895449
85978263750717485668458407718537841810503168698812392372532335935
83219206555043774166755681858313621909827409674365639855267171085
58614134434477224688105247341703364940790494240106925439963808186
78491502361782954524767478143593895381808766230716183766845428565
24326680629726906263789771769536673205252717593838391265082379437
59773650739285645856030501090796011587386148607013824314152676927
74218651718647063080895712849599805325468580261808680812235865761
57614719566590823657659445527636582501346480710062983713653361005
92559775777123591718933004262206968820533549794376761848463423794
82668816672878082887827672491680706425638359990485336743555195895
05737729902610502726216835060623074435123714916576141842287647588
56873876170667444955960567600029343902997256650693396650636503676
59535178388869210715798225289233530602862034069794578375621193301
96803484493096849459868239604074741980710055770035999078504264593
98202941354027066327946405286094639000203935695465640923608173728
37219399394658720878896059728151605838238676541669512380743569758
35870185837737111725988878053695789542180692987819699112326070401
27479688885038589358818473994371118835771187973352136635190063633
56336125505919740919820037511002378906574695952324863553936871927
84657620858665917551159447158076508959705121765260355030990486845
42495579690378139565635944829974933348972932826334172679265166631
099735

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  Subject Author Date
Solutioncomputer solutionCharlie2023-04-27 08:56:35
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