Related papers: The On-Line Encyclopedia of Integer Sequences
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…
We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…
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.
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.…
We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…
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…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
The sequence A000975 in OEIS can be defined by $A_1=1$, $A_{n+1}=2A_n$ if $n$ is odd, and $A_{n+1}=2A_n+1$ if $n$ is even. This sequence satisfies other recurrence relations, admits some closed formulas, and is known to enumerate several…
Infinite sequences are of tremendous theoretical and practical importance, and in the Information Age sequences of 0s and 1s are of particular interest. Over the past century, the field of symbolic dynamics has developed to study sequences…
Open Information Extraction (OpenIE) facilitates domain-independent discovery of relational facts from large corpora. The technique well suits many open-world natural language understanding scenarios, such as automatic knowledge base…
Extending earlier work of R. Donaghey and P. J. Cameron, we investigate some canonical "eigen-sequences" associated with transformations of integer sequences. Several known sequences appear in a new setting: for instance the sequences (such…
In this paper, we begin by discussing different types of preference profiles related to the stable marriage problem. We then introduce the concept of soulmates, which are a man and a woman who rank each other first. Inversely, we examine…
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.
Using three supercomputers, we broke a record set in 2011, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in Online Encyclopedia of Integer Sequences (OEIS), to achieve the number for 4-regular…
Sequential neuronal activity underlies a wide range of processes in the brain. Neuroscientific evidence for neuronal sequences has been reported in domains as diverse as perception, motor control, speech, spatial navigation and memory.…
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…
We provide a rigorous Bayesian formulation of the EIT problem in an infinite dimensional setting, leading to well-posedness in the Hellinger metric with respect to the data. We focus particularly on the reconstruction of binary fields where…
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.
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
Neural Networks (NNs) have provided state-of-the-art results for many challenging machine learning tasks such as detection, regression and classification across the domains of computer vision, speech recognition and natural language…