Michael Thomas De Vlieger, St. Louis, Missouri, written 2021 0120, updated 2024 0207.
This page links many of the mathematics papers that I’ve written, listed in reverse chronological order. Each paper includes Mathematica code and tends to engage content at the OEIS, with all sequences listed in the “Concerns Sequences” section at the end of the paper. I track changes to the papers, especially when they are works in progress. Much of the work before 2020 was devoted to the service of audiences interested in the mathematics of number bases. A large body of papers came about in the wake of the corona lockdowns such that now it makes sense to have an index to access them all. In 2023 all papers appear as PDFs with an abstract page. At the end of the year a compendium of the papers will be posted.
Integer sequences that are analyzed but do not appear in OEIS are often given a number s (for “sequence”) followed by the big-endian Gregorian date (ISO 8601 basic format). If these are accepted by OEIS, if and when they are posed, their addresses will change here to reflect and support the OEIS A-number. If the OEIS delists a sequence, we shall continue to refer to it as “former” A-number. The dates in the brief abstracts below are written in military fashion and eliminate the century, thus, in place of writing 2021 0120, we write 210120.
Simple Sequence Analysis is NOT peer reviewed and I am an amateur mathematician. The subject of the publication is merely those sequences about which I and others have thought about, accompanied by elementary theorems, graph studies, and conjectures. I post Mathematica code in most papers and am happy to share what I’ve done so you can also explore. The truth about this “publication” is that it is probably very nearly a junk journal. Perhaps it’s like a mathematical garage band. Be sure to let me know what you think, especially if I have made any errors. I can’t really be too embarrassed because I am an amateur, but that means I need to be extra careful what I write is true.
If you have a sequence and want analysis I’ll usually gladly conduct it around any work I have to perform. It takes about 10-40 work hours to do a good job. The CAS I employ is Wolfram Mathematica.
Click a link at left in the lists below to view the desired work. Items in bold are major works.
2023:
A369609. Divisibility Based Lexically Earliest Sequence
with Cellular Automaton Behavior (PDF) (Sycamore 240314).
A366250. Relationship of Complementary Divisors rad(k) and k/rad(k) (PDF) (Munn 240207).
A369690. On A369690(n) = max(A119288(n), A053669(n)) (PDF) (Munn 240202).
SA20240106. Partitioning the Set of Tantus Numbers (240106, in progress).
2023:
A368507. Powers of Superprimorials (PDF) (231227).
A366825. Minimally Tantus Numbers (PDF) (231220).
A367188. (PDF) (Sycamore 231111).
A365000. Lexically Earliest Sequences using Regular and Coregular Numbers (Sycamore 230824)
A363920. On A113901 = Ω(n)ω(n) and A363920 = nA113901(n). (PDF) (Luschny 230720).
A363923. Sequences relating Ω(n), ω(n), and rad(n). (PDF) (Luschny 230711).
A362041. On trying to exceed θ(P(n+1)) with θ(k) where k is prime(n) smooth. (PDF) (230623).
A363061. Constitutive Counting Functions for Primorials. (PDF) (230621).
A362041. The NextRegular(n) Function. (PDF) (230621).
S20230321. A Symmetrically Semicoprime Case Related to Størmer and Gersonides. (230321).
S20230226. Constitutive State Counting Functions. (PDF) (230226).
S20230225. The Semitotative Counting Function and Species. (PDF) (230308).
S20230223. The Semidivisor Counting Function and Species. (230223).
S20230222. The Symmetric Semitotative Counting Function A360480. (PDF) (230222).
S20230216. The Symmetric Semidivisor Counting Function A355432. (PDF) (230216).
S20230212. The Ever-Late Sequence. (PDF) (Sycamore 230212).
S20230211. (PDF) (Sycamore 230211).
On the Completely Regular Scaling Issue. (Abstract, PDF) (230202).
A357910. (PDF) Extending A019565 to create a permutation of natural numbers. (230127).
Constitutive Basics. (PDF) Overview of constitutive states and relations. (230125).
A036998. (PDF) Partition counting function restricted to distinct totatives. (Meeussen 230124).
S20230119 & S20230120. (PDF). Study of 2 LES based on symmetric difference among sets of prime divisors (Sycamore 230119).
A359557. (PDF) The Raise-the-Bar Sequence. (Shannon 230111).
2022:
A359369. (PDF) The Fishnet Sequence. (Sycamore 221227).
A358174. Consecutive numbers of a certain omega-multiplicity species. (221123).
A358268. First n-bit numbers in the Van Eck sequence. (221105).
A356322. Consecutive tantus numbers (221028).
A120944, A126706, & A246547. Omega multiplicity classes (220518).
A353916 & A353917. Constitutively restrained versions of the EKG sequence (220517).
A353125. An inventory sequence with integer log payload. (Sycamore 220508).
A352867. The Catch-Up Sequence. (Shannon, 220406).
A085229. Sequences beginning with 1 and the first ℓ odd primes, thereafter pairwise coprime between the (ℓ−1) most recent terms. (Various, 220422).
A119435. Theorems regarding minima and maxima. (Quet 060519, 220420).
A350014. Numbers n such that τ(n) is coprime to primorials. (220117, 221208).
A350877. The Sisyphus Sequence. (Angelini-Dubois, 220122).
A350768. Cardinality of Cardinalities Sequence. (Sycamore, 220115, in progress).
A098550: The Yellowstone Sequence (Zumkeller, 040914, in draft).
2021:
A350359. The Sandwich Sequence. (Sycamore, 211226).
A350150. (Sycamore, 211215).
A064413: The EKG Sequence. (Ayres, 010930).
Constitutive relations (211122). Revision of 190628 article.
s20211102: The Doorman Sequence. (Sycamore, 210725).
A347062: The Follower Inventory Sequence. (Sycamore, 211017).
A348328: Recordbearing Inventory Sequence. (Sycamore, 211011).
A128331: Recursive Totient Sequence. (Sycamore, 211006; Quet 070504).
A114897: Recursive range prime counting function sequences. (Quet et al., 210930).
A347113. (Olson, 210902, in progress).
A136417. (210804, in progress).
s20210701: The Marlin Sequence. (210701).
s20210625: The Sailboat Sequence. (Sycamore, 210625, in progress).
s20210622: The Gorgeous Sequence. (Sycamore, 210622).
s20210620: Payload and counter multiplier sequences. (Sycamore, 210618).
A345147 The Cliffside Sequence (Sycamore, 210605).
A343887: The Once-and-Nevermore Sequence (Sycamore, 210502, in progress).
s20210408: Icarus revisited (Sycamore, 210408).
A342909: A bifurcated self-referential counting function (Sycamore, 210316).
A343327: Self-referential τ trajectories (Sycamore, 210321).
s20210315: Self-referential σ trajectories (Sycamore, 210315).
A342616: A self-referential, internal divisor counting function sequence (210317).
s20210303: The Flight and Demise of Icarus (Sycamore, 210303).
A341679: A self-referential divisor-seeking sequence (Shannon, 210302).
s20210228: The “Overxeroxed” Sequence (Sycamore, 210301).
A181391: The Van Eck Sequence (210214, in progress).
A341351: A048653(A181815(n)) (Karttunen, 210210).
s20210203: The “Exceeding-Spacing” Sequence (Sycamore, 210203).
A341130: The “Relay Race” Sequence (Beard, 210205).
A340840: Relationship of Highly Composite and Superabundant Numbers (201231).
s20210116: The “One-by-One” Sequence and variant (Sycamore, 210116).
s20210114: Self-referential counting sequences based on elementary number-theoretical counting functions.
A181815: Interpret the conjugate of multiplicity notation as indices of prime divisors (Vandermast, 210115).
A347284: The “Idaho” Sequence (Sycamore, 20210106).
2020:
A322182: The “Lazy Racer” Sequence (Rémy Sigrist, 201220).
s20201216: The “Once and Again” Sequence (Sycamore).
A279818: The “Paint Sprayer” Sequence (Sycamore, 201202).
s20201118: On a recursive coprimality sequence (Sycamore).
A338944: Chains of Nearly Doubled Primes / Cunningham Chains (201117).
A336893: Sum of digits coprime to catenation (Sycamore, 201111).
A336683: Fibonacci(n) mod m and Lucas(n) mod m (201017, unfinished)
A338209: The Word→Least, Word→Most, and Word→Any sequences (201016).
A338191: The Root→Least, Root→Most, and Root→Any sequences (Sycamore, 201015).
A340138 : The “Frayed Rope” Sequence (Sycamore, 201008).
A160136: Deléham’s “lodumo” transform of the Fibonacci sequence mod m (201001).
A008336: An examination of the Recamán sequence OEIS A008336, inspired by Shannon’s A337486 (200912)
Former A337099: The “Prime Horizon Sequence (Sycamore, 200826)
A330170: 2n + 3n + 6n − 1 (200730)
Former A335807: On the Schuster Sequences (Schuster, 200701)
A334769: Central zero-triangles in rotationally symmetrical XOR-Triangles (200512).
A334468: A transformation of A217827 (200501).
A334144: Hasse Diagrams of the “Wichita” function. (Wilson, Karttunen, Kagey, 200416)
A334144: The
“Wichita” lattice (Wilson, 200416).
A333238: Distinct Least Primes of Prime Partitions of n (Sycamore, 200328)
2019: (Primarily on the subject of number bases)
Divisibility Test / OEIS A307540 (190705).
The Constitutive Arithmetic Functions (190628).
Tau vs. rcf: The divisor and regular counting functions (190628).
Natural Fractions and Gradus Suavitatis (190627).
Quasinumerals (190619).
Threefoldness (Volan, 190205).
Surrogation (regarding number bases, 190202).
2018:
A301414: On a graph of the divisors (pω(m)#, m/pω(m)) of highly composite numbers m (180328).
A301892: On the regular counting function applied to the highly composite numbers (180328).
A051953: Concordance across sequences relating to nondivisors in the cototient of n (180316)
A300859: Decomposition of terms in A300859 and Related Sequences (180315).
A300860: Decomposition of terms in A300860 and Related Sequences (180314).
A299990: Examination of the relationships of the species of numbers enumerated in A010846 (180226).
2017:
A295221: Prime decomposition of terms in A295221 (171122).
A293555: Records A293556 and their indices A293555 in A243822 (171117).
A292867: Analysis of Records (A292868) and Indices of Records (A292867) in A243823 (171117).
A288813: Relations between A288813, A288784, A002110, and A244052 (170715).
A288784: Relations between A288784, A002110, A060735, and A244052 (170702).
A288813: Maximum “Distension’ i Given ‘Tier’ m and ‘Depth’ j, (170626).
A288813: Number of terms of A288813 that have j = m − π(A053669(A288813(m))) + 1, (170626).
A288784: Computation of A288813 via directed iteration of A287352(A002110(n)), (170626).
Turbulent Candidates (A244052, 170226)
2014:
A010846: Regular numbers k | ne for e > 0 (140813).
A066272: Arithmetic Relationships between Antidivisors k < n and n. (140812).
2011:
Using Number Bases as Tools, ACM Inroads Magazine, Vol. 3 Issue 1, March 2012. DOI: 10.1145/2077808.2077809.
Neutral numbers, Necessarily composite nondivisors in the cototient of n (111022).
I generally love elementary number theory though far from a luminary of mathematics. This said, I offer the following acknowledgements.
I thank my father, who bought me an Apple II+ in December 1980, so I could program in basic at age 10, and a Macintosh in December 1984, so I might continue and hack programs in ResEdit throughout my teen years. Without his guidance none of what I have done since then would’ve been conceivable.
Thanks are in order for Dr. Neil Sloane and the editors of the OEIS, and certain individuals, principally, Antti Karttunen, David Sycamore, Jamie Morken, Robert G. Wilson V, and Peter Kagey in collaboration regarding several of the latter works. I also thank Dr. John Impagliazzo (Hofstra Univ.), Prof. Jay Schiffman (Rowan Univ.), and Prof. Gene Zirkel (Nassau Community College) for their encouragement in mathematics. I thank my Aunt Katherine (Mary Nuzzo, passed away in 2018), a computer scientist of the 60s and 70s, for encouraging me in mathematics and programming, putting me on to duodecimal notation. Finally, I thank Mrs. Betty Svitek (departed), my middle school math teacher for enrichment in algebra and number bases, and general encouragement in mathematics that form the basis of all I've done since then.
I humbly dedicate this page to the memory of Prof. Gene Zirkel who has passed away in 2018.
Michael Thomas De Vlieger,
St. Louis, Missouri, 2021 0121.
Updated 2024 0207 1900.