Related papers: The On-Line Encyclopedia of Integer Sequences
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…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
In an automatic search, we found conjectural recurrences for some sequences in the OEIS that were not previously recognized as being D-finite. In some cases, we are able to prove the conjectured recurrence. In some cases, we are not able to…
A non-self OU sequence is a cyclic sequence of crossing information of non-self crossings that is obtained by traversing a knot component of an oriented link diagram. In this paper, we investigate what information can be derived from…
With the abundant amount of available online and offline text data, there arises a crucial need to extract the relation between phrases and summarize the main content of each document in a few words. For this purpose, there have been many…
When my "Handbook of Integer Sequences" came out in 1973, Philip Morrison gave it an enthusiastic review in the Scientific American and Martin Gardner was kind enough to say in his Mathematical Games column that "every recreational…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
Indicators of Compromise (IOCs) are artifacts observed on a network or in an operating system that can be utilized to indicate a computer intrusion and detect cyber-attacks in an early stage. Thus, they exert an important role in the field…
An event structure is a mathematical abstraction modeling concepts as causality, conflict and concurrency between events. While many other mathematical structures, including groups, topological spaces, rings, abound with algorithms and…
We describe the results of the computation of aliquot sequences with small starting values. In particular all sequences with starting values less than a million have been computed until either termination occurred (at 1 or a cycle), or an…
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…
A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1} <= 2 t_i. A "Meeussen sequence" is an increasing sequence of positive integers (m_1,m_2,...) such that m_1=1, every nonnegative…
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…
We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent…
This paper investigates a variant of the famous "happy numbers" sequence, given by A351327 on the oeis. First of all we'll define this integer sequence, and then we'll show some important results about it; in particular we conjectured that…
Information Extraction (IE) refers to automatically extracting structured relation tuples from unstructured texts. Common IE solutions, including Relation Extraction (RE) and open IE systems, can hardly handle cross-sentence tuples, and are…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
Tight bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources are derived. A pattern of a sequence is a sequence of integer indices with each index representing the order of…
Open Information Extraction (OpenIE) is a fundamental yet challenging task in Natural Language Processing, which involves extracting all triples (subject, predicate, object) from a given sentence. While labeling-based methods have their…
In this tribute to Neil Sloane, we revisit the first sequence in the On-Line Encyclopedia of Integer Sequences, sequence A435 (1, 8, 78, 944, 13800, 237432, 4708144, 105822432, ...), that he encountered when he was a graduate student, and…