Article Index


Carréphylic classes: n2+1

Here are the first 10 carréphylic numbers of the form n2+1 with the usual data. The qt-blocks in the middle split the sections in a left part below and right part above the root-value. For all q/t fractions v=-1.
A fraction for which v=-1 is always a q/t fraction, always in the middle, and constitutes the only occasion where the denominator of the next fraction in a section surpasses the numerator of the previous one, in carréphylic as well as carréphocic numbers.
To understand the nature of the exception one would have to understand the nature of the rule, which is that the next denominator at most equals the previous numerator, and that only in the sp-blocks. The explanations of both rule and exception have till now eluded me.

√2
1013471724419914023957781613933363475681191960127720473211142431615642758076658579416641607521388089954884209369319226195373198885654608393131836323186444716...
011235121729709916940857798523783363574113860196013346180782114243195025470832665857113668927442103880899662510915994428226195373861396593222358131836323...

√5
10127920293812316136052168222072889646093491223839603518411159201677612196027106479302492080100301034939405981275204316692641373258805401852170711162228826127299537289669785740...
011134913175572161233305987129228894181547317711231845184175025982093178114160209302491346269176228957028877465176166926412415781731622993102334155133957148299537289...

√10
1012313161960799811748760472122803001372244431849322936273798658011395914133816871770224787096410396813287760432744153671226406803266668933307369639480499124848300...
0111145619253137154191228721949117714055848725386582737936037446955335322207027542332877610396811368457169723320260098432812104588211248483039480499...

√17
1012342125293313616920223526813731641190921778976111531333015507176849059710828112596514364959228073592987957810232271166876597802971449058311781947865739081504...
01111156783341495765333398463528217727053233376142892197326262305513484014364917848921332924816928300914498851732894201590322989129478657...

√26
10123453136414651260311362413464515314136564171468652012652031721369224212347324525253203513728764254014779265304512704780323523137656824296133482658453570353267266138029696433867314874376654100801275861040...
011111167891051617181911016167178189191020520162217241826192811030162826731278342893729104030530451634481738511842541946571105060164076367458237850883895594391061004054100801...

√37
101234564349556167734445175906637368098826247712980118893977510657648247548186138967951074521181091287669120191040785116955112983171427083155584994638601101970912575558141314071568725617243105187989541331485271519474811707464351895453892083443432271432971381658736...
01111111789101112738597109121133145102711721317146216071752106571240914161159131766519417211691499351711041922732134422346112557801555849181162920674092323189257896928347493090529218894832498001228070541311610703425159937342128227143297...

√50
10123456757647178859299700799898997109611951294139311243126361402915422168151820819601138600158201177802197403217004236605256206275807222605725018642777671305347833292853605092388089927442100313229993520389839084797429656964684659550727494546083934407480434953564365499648296045732226591816157137900087683984015433397200...
0111111118910111213149911312714115516918319715901787198421812378257527721960122373251452791730689334613623339005314812353817392822431827470832509837548842388089944297414978583552742560762676625109717395177227936233118670053979777767728549956593222358100945151108667944768398401...

√65
1012345678738189971051131211291040116912981427155616851814194320721877720849229212499327065291373120933281268320...
01111111119101112131415161291451611771932092252412572329258628433100335736143871412833281...

√82
10123456789911001091181271361451541631476163918021965212822912454261727802943295933253635479384224136544308472515019453137481176...
0111111111110111213141516171816318119921723525327128930732532683593391842434568489352185543586853137...

√101
10123456789101111211311411511611711811912012020222124222623282430253226342736283829403044531485615259156621606516468168711727417677180801812040...
01111111111111121314151617181920201221241261281301321341361381401443148325233563460356436683772387639804080801...