Related papers: Another Set of Sequences, Sub-Sequences, and Seque…
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,…
74 new integer sequences are introduced in number theory, and for each of them is given a characterization, followed by open problems. each one a general question: how many primes each sequence 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.…
This paper gives a brief description of the author's database of integer sequences, now over 35 years old, together with a selection of a few of the most interesting sequences in the table. Many unsolved problems are mentioned.
In this paper we present many congruences for several Ap\'ery-like sequences.
We count the number of subsets of $\{1,2,\cdots,n\}$ under different conditions and study the sequence obtained as we let $n$ increase.
In this paper a small survey is presented on fourteen sequences, such as: G Add-on Sequences, Sieve Sequences, Digital Sequences, Non-Arithmetic Progressions, recreational sequences (Lucky…
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…
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…
Scattered sequences are a generalization of scattered polynomials. So far, only scattered sequences of order one and two have been constructed. In this paper an infinite family of scattered sequences of order three is obtained. Equivalence…
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…
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,…
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem…
A family of sequences produced by a non-homogeneous linear recurrence formula derived from the geometry of circles inscribed in lenses is introduced and studied. Mysterious ``underground'' sequences underlying them are discovered in this…
Sequence A000975 in the Online Encyclopedia of Integer Sequences (OEIS) starts out 1, 2, 5, 10, 21, 42, 85, ... . As of July 1, 2016, the description in the OEIS lists several characterizations of this sequence and numerous examples of…
First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will…
In this paper we present 43 new inequalities related to integer part and fractional part.
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
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…