Related papers: "A Handbook of Integer Sequences" Fifty Years Late…

The Oldenburger-Kolakoski sequence is the only infinite sequence over the alphabet $\{1,2\}$ that starts with $1$ and is its own run-length encoding. In the present work, we take a step back from this largely known and studied sequence by…

Cryptography, derived from Greek meaning hidden writing, uses mathematical techniques to secure information by converting it into an unreadable format. While cryptography as a science began around 100 years ago, its roots trace back to…

Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the…

A sequence $(a_1, \ldots, a_n)$ of nonnegative integers is an {\em ascent sequence} if $a_0 =0$ and for all $i \geq 2$, $a_i$ is at most 1 plus the number of ascents in $(a_1, \ldots, a_{i-1})$. Ascent sequences were introduced by…

Dyck paths (also balanced brackets and Dyck words) are among the most heavily studied Catalan families. This paper is a continuation of [2, 3, 4]. In the paper we are dealing with the numbering of Dyck paths, with the resulting numbers, the…

Natural numbers from 0 to 11111 are written in terms of 1 to 9 in two different ways. The first one in increasing order of 1 to 9, and the second one in decreasing order. This is done by using the operations of addition, multiplication,…

The growth of big-data sectors such as the Internet of Things (IoT) generates enormous volumes of data. As IoT devices generate a vast volume of time-series data, the Time Series Database (TSDB) popularity has grown alongside the rise of…

Geometric sequences are found documented as early as 300BC in the text, Book IX of Elements written by Euclid of Alexandria. In this paper a new principle for identities involving the product of any k-number of terms of a geometric sequence…

In-place associative integer sorting technique was developed, improved and specialized for distinct integers. The technique is suitable for integer sorting. Hence, given a list S of n integers S[0...n-1], the technique sorts the integers in…

The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.

We investigate a method of generating a graph $G=(V,E)$ out of an ordered list of $n$ distinct real numbers $a_1, \dots, a_n$. These graphs can be used to test for the presence of interesting structure in the sequence. We describe sequences…

In this paper we study the prevalence of unique entity identifiers on the Web. These are, e.g., ISBNs (for books), GTINs (for commercial products), DOIs (for documents), email addresses, and others. We show how these identifiers can be…

Analysing historical patterns of artificial intelligence (AI) adoption can inform decisions about AI capability uplift, but research to date has provided a limited view of AI adoption across various fields of research. In this study we…

In this paper we show that two of the Worpitzky Number Triangles, OEIS A028246 and A019538, may each be used in look-up table fashion, along with specific diagonals of a polynomial sequence's difference triangle to easily solve for the…

The present research attempts to identify the impact of retracted papers on previous or subsequent papers. We consider the 5693 retracted papers from 1975 to 2020 indexed in the Web of Science database based on bibliometric methods. We use…

In this paper, we perform an arithmetization of well-formed parenthesis strings with zeros (Motzkin words) and of corresponding Motzkin paths. The transformations used are reminiscent of G\"odel numbering for mathematical objects of some…

The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now is growing at a healthy rate. This chapter, for the {\it Highly Structured Stochastic Systems} book (Oxford University Press, 2003)…

Science is a social process with far-reaching impact on our modern society. In the recent years, for the first time we are able to scientifically study the science itself. This is enabled by massive amounts of data on scientific…

We introduce a self-learning algorithm for synthesizing programs for OEIS sequences. The algorithm starts from scratch initially generating programs at random. Then it runs many iterations of a self-learning loop that interleaves (i)…

Research in secure multi-party computation using a deck of playing cards, often called card-based cryptography, dates back to 1989 when Den Boer introduced the "five-card trick" to compute the logical AND function. Since then, many…