Related papers: My Favorite Integer Sequences
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
In this paper 101 new integer sequences, sub-sequences, and sequences of sequences, together with related unsolved problems and conjectures, are presented. Also, definitions, examples, solved or open questions, and references for each…
We describe an online database of number fields which accompanies this paper The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on summarizing tables and connections to…
This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of…
We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia…
Until 1973 there was no database of integer sequences. Someone coming across the sequence 1, 2, 4, 9, 21, 51, 127,... would have had no way of discovering that it had been studied since 1870 (today these are called the Motzkin numbers, and…
This article gives a brief introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms…
A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.
This article investigates integer sequences that partition the sequence into blocks of various lengths - irregular arrays. The main result of the article is explicit formulas for numbering of irregular arrays. A generalization of Cantor…
This is a structured compilation of some of my favourite open problems.
In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences,…
What follows is the story of a family of integer sequences, which started life as a Google interview puzzle back in the previous century when VHS video tapes were in use.
The purpose of this memoir is to discuss two very interesting properties of integer sequences. One is the law of apparition and the other is the law of repetition. Both have been extensively studied by mathematicians such as Ward, Lucas,…
There are several standard procedures used to create new sequences from a given sequence or from a given pair of sequences. In this paper I discuss the most popular of these procedures. For each procedure, I give a definition and provide…
The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…
In this paper, we prove the finiteness of the number of integer solutions of the decomposable form inequalities. We also study the number of integer solutions of a sequence of decomposable form inequalities.
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
The recent history of The On-Line Encyclopedia of Integer Sequences (or OEIS), describing developments since 2009, and discussing recent sequences involving interesting unsolved problems and in many cases spectacular illustrations. These…
A consistent query answer in an inconsistent database is an answer obtained in every (minimal) repair. The repairs are obtained by resolving all conflicts in all possible ways. Often, however, the user is able to provide a preference on how…