by Michael Thomas De Vlieger, 13 August 2014, St. Louis, Missouri. Revised 5 October 2020.
This small set of pages contains some of my work in mathematics. I am an amateur elementary number theorist, armed with Mathematica 11.3 and a growing capability in Wolfram Language. I came to mathematics via number bases. The Online Encyclopedia of Integer Sequences has been an early influence on me, through mentions of Sloane’s A#### in math texts of the last century. I am happy to be a contributor to the OEIS (I’ve authored over 150 sequences and collaborated on an additional 30. Read about them here). I've written some sequences, contributed data files and Wolfram code to others. You can read more about “Why Mike is into Math” here.
Here are some pages on this site. I will find a better way to link these as I go on.
Neutral numbers (numbers m ≤ n that neither divide n nor are coprime to n). I am not sure I "discovered" two kinds of neutrals but they surely have fascinated me. (Wolfram code updated 9 January 2015)
Anti-divisors. Proofs that show odd anti-divisors m must be coprime to n, etc. (Updated 9 January 2015)
Arithmetic map. These are what many friends in math know me for; my charts of arithmetic relationships. This is what pulled me into number theory.
Data briefs: (Many of these are text files that I am converting to HTML)
A244052: About highly regular numbers, numbers that set records in A010846(n). (2014), revised 2017 0619. (local text)
A288784: “Relations between A288784, A002110, A060735, and A244052”, 2 July 2014, updated 2017 0721. (text)
A288784: “Tree associated with computation of terms of A288813 via directed iteration of A287352(A002110(n))”, 2017 0626. (local text)
A288813: “Relations between A288813, A288784, A002110, and A244052”, 2017 0715. (text)
A288813: “Number of terms of A288813 that have j = m − π(A053669(A288813(m))) + 1”, 2017 0626. (local text)
A288813: “Maximum “Distension’ i Given ‘Tier’ m and ‘Depth’ j (for terms in A288813)”, 2017 0626. (local text)
A292867: “Analysis of Records (A292868) and Indices of Records (A292867) in A243823”, 2017 1117.
(text).
A293555: “Records A293556 and their indices A293555 in A243822”, 2017 1117. (text)
A295221: “Prime decomposition of terms in A295221” (Numbers n such that 2 × A243823(n) = n), 2017 1122. (text)
A299990: “Examination of the relationships of the species of numbers enumerated in A010846”, 2018 0226. (text)
A300860: “Decomposition of terms in A300860 and Related Sequences”, 2018 0314. (text)
A300859: “Decomposition of terms in A300859 and Related Sequences.”, 2018 0315. (text)
Concordance across sequences relating to nondivisors in the cototient of n. (text)
A301892: “On the regular counting function applied to the highly composite numbers.”
A301414: “On the graph of highly composite numbers as products of primorials.” 2018 0418.
A333238: Irregular triangle with row n lists the distinct least primes p of the prime partitions λ of n.
A333337: Positions of rows of n consecutive smallest primes in A333238.
A334144: Hasse Diagrams of the “Wichita” function.
A334468: Primitive terms that are smallest numbers m = n + k that are k-smooth for k in A217287.
A334769: Central zero-triangles in rotationally symmetrical XOR-Triangles.
A335807: Absolute differences of prime pairs {p, q} with p > 5 and q ≠ p where all p and q are distinct, such that p + q ≡ 0 (mod 10).
A330170:
2n + 3n + 6n − 1.
A008336: On the plot of the multiplicities of the multiplicative Recamán sequence.
A160136: On the “lodumo” transform of the Fibonacci sequence mod m.
Articles:
Using Number Bases as Tools, ACM Inroads Magazine, Vol. 3 Issue 1, March 2012. doi: 10.1145/2077808.2077809.
This site is not as flashy as my main business site, nor my art site. Somehow I am at a sort of "triple point" of creativity, spirituality, and analytics; I am also a devoted husband and father and an avid competitive swimmer. I feel terrifically balanced. Something tells me that, had I gone into engineering or mathematics, I would be a notable painter or novelist. Since I create for a living, my refuge is in mathematics.
I had a stalled project called Numberbases.com, which will now perhaps become the receptacle for this work.
Best regards, Michael
(Updated 5 October 2020)