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s7836The Rykami Argam Sketchbook |
The Totative Page and the Prime Reference Page
The right page, “The Prime Reference Page”, reproduces the “Primes in Sexagesimal Scale” table at s7836a53, extending the set to include all primes less than 2580. The primes, written in sexagesimal argam, are arranged (mod 60) and fall into one of 16 possible residues. This table,“Primes in Sexagesimal Scale, Arranged by Sexagesimal Totatives”, was started 10 July 2007, Tayya 79ab, seven dozen ninth phase (Salcyra-Karlmelal Xrga, “life phase of Karl Michael, Son”), St. Louis. It was finished in early January 2008.
This page was remastered in Wolfram Mathematica 6 July 2018 (tayya a195) and appears below.
The left page, “The Totative Page”, summarizes observations regarding digits t that are coprime to bases r, i.e., gcd(t, r) = 1. The totatives of bases {2, 6, 8, 9, 10, 12, 14, 16, 60, 120, 360} are paired with their additive complements and indicated in cyclic diagrams. In studies that led up to the Rykami Argam, I realized totatives constitute a second major consideration in the utility of number bases, primarily as resistance to human computation. I studied sexagesimal totatives at s7836a12 and s7836a53, as they tended to restrict the occurrence of primes (mod 60). The pages s7836a07 and s7836a08 examine how primorials and prime factorization impact the totient ratio. My recognition that totatives represent a restraint for human leverage of a number base had been intense enough by mid 2007 that it was regarded with disdain by my mentor Prof. Gene Zirkel. Totatives form a strong element in the 100+ page, 6½ megabyte PDF manual d7a60. Totatives are evaluated in the 2010 “Balance Study”, a 1¾ Mb PDF d8483. Totatives are indicated in gray in digit maps illustrated in “Digit Base Relationship”, 2 Mb PDF d87a9 and the subsequent 11 Mb PDF presentation d8614. The 2011 paper “Neutral Digits” recognize the totative relationship as cardinal and canonical, helping to define neutral digits in the 1.15 Mb PDF d8895. Totatives are mentioned in the November 2011 paper “Dozenal FAQs”, a 5½ Mb PDF presentation d8907. The left page took shape 29 December 2007, Tayya 7b13, seven dozen eleventh phase (Salcyra-Lectajinal Xrga, “life phase of the Virtual Solid Order”), St. Louis.
This page last modified Friday 6 July 2018.