Related papers: The On-Line Encyclopedia of Integer Sequences
In his July 1974 Scientific American column, Martin Gardner mentioned the Handbook of Integer Sequences, which then contained 2372 sequences. Today the On-Line Encyclopedia of Integer Sequences (the OEIS) contains 140000 sequences. This…
Operators on probability distributions can be expressed as operators on the associated moment sequences, and so correspond to operators on integer sequences. Thus, there is an opportunity to apply each theory to the other. Moreover,…
The OEIS sequence A051221 consists of nonnegative integers of the form 10^x - y^2. The known values are those less than or equal to 2000 with x <= 7, and it is conjectured that no new values in this range appear for x >= 8. In this paper,…
An Inventory Sequence $(S_0, S_1, S_2, ...)$ is the iteration of the map $f$ defined roughly by taking an integer to its numericized description (e.g. $f(1381)=211318$ since "$1381$" has two $1$'s, one $3$, and one $8$). Our work analyzes…
We compute the next few terms of the OEIS sequence A348456 and provide guessed equations for the generating functions of some sequences in its context.
Indexes are the best apposite choice for quickly retrieving the records. This is nothing but cutting down the number of Disk IO. Instead of scanning the complete table for the results, we can decrease the number of IO's or page fetches…
Advances in Web technology enable personalization proxies that assist users in satisfying their complex information monitoring and aggregation needs through the repeated querying of multiple volatile data sources. Such proxies face a…
This article focuses on the complicated yet still relatively immature area of the Internet of Things Search Engines (IoTSE). It introduces related concepts of IoTSE and a model called meta-path to describe and classify IoTSE systems based…
We define impulse response sequence in the set of all linear recurring sequences satisfying a linear recurrence relation of order $r$. The generating function and expression of the impulse response sequence are presented. Some identities of…
Inference on time series data is a common requirement in many scientific disciplines and internet of things (IoT) applications, yet there are few resources available to domain scientists to easily, robustly, and repeatably build such…
Software testing is presented as a so-called theme within which different authors and groups have defined different subjects each of these subjects having a different focus on testing. A uniform concept of software testing is non-existent…
We defined numbers of the form $p\cdot a^2$ as SP numbers (Square-Prime numbers) ($a\neq1$, $p$ prime) in 'Distribution of Square-Prime Numbers' (arXiv:2109.10238). These numbers are listed in the OEIS as A228056. Some examples of SP…
Online sequence prediction is the problem of predicting the next element of a sequence given previous elements. This problem has been extensively studied in the context of individual sequence prediction, where no prior assumptions are made…
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…
An elementary method for computing various prime sequences using the sequence of Farey sequences is described.
Formal synthesis is the process of generating a program satisfying a high-level formal specification. In recent times, effective formal synthesis methods have been proposed based on the use of inductive learning. We refer to this class of…
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…
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.
A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by…
This paper presents a syntactic lexicon for English that was originally derived from the Oxford Advanced Learner's Dictionary and the Oxford Dictionary of Current Idiomatic English, and then modified and augmented by hand. There are more…