Article Index


Carréphylic classes: n2-n/2 (for even n)

Here are the first 6 carréphylic numbers of the form n2-n/2 (for even n) with the usual data.
Root-3 is a 'small numbers exception' on the general pattern because it is also a member of n2-1 and shows the characteristic 'sp-block shift' of that class.
The first non-trivial ab-blocks (second for root-3) follow a simple pattern (4n-1)/4. The s/p- and t/q-fractions are the only ones above the root-value.
The values 'v' equal half the numerator of the first t/q fraction and the numerator of the first q/t fraction respectively.

√3
10123571219264571971682653626279891351234036915042873313775188173259251409702261216351918612620874539487160359781221694157...
01112347111526415697153209362571780135121312911504279531086418817296814054570226110771151316262087413403564719978122...

√14
101234711155671861011162173334491680212925783027347665039979134555034463799772549070910416419487329903740320115086401911841231504227182433121444583968789611311208257545208856...
011111234151923273158891204495696898099291738266735961345517051206472424327839520827992110776040320151096161872172648183424115607222394963322920412082575...

√33
1012345611172313215517820122424727051778710576072712981869243103001135712414237713618548599279180327779376378424977473576522175570774109294916637232234497128362081507070517305202195396992177419624008693262431905025188376495073102738263590186388...
011111112342327313539434790137184105712411425160917931977216141386299846048599570596551973979824399089999359190258289617388976223449726234733012449340142537904014179377456835387477301331608317884436102738263...

√60
1012345678152331240271302333364395426457488945143319211488016801187222064322564244852640628327302485857588823119071922320104139111604621279533139860415176751636746175581718748883630705550559373804815716896064549441719299227931040386690884940713651014518461088323271162128082250451353412579434574707513543553200...
011111111123431353943475155596312218524819212169241726652913316134093657390575621146715372119071134443149815165187180559195931211303226675242047468659710769952816738048183332979286113102389291119174512144561130973771405019315003009290453914405621159059220457470751...

√95
101234567891019293938041945849753657561465369273177015012271304129640...
01111111111123439434751555963677175791542333123041...

√138
1012345678910111223354755259964669374078783488192897510221069111621853301441751888...
01111111111111234475155596367717579838791951862813764417...