Related papers: "A Handbook of Integer Sequences" Fifty Years Late…
Stanley and Odlyzko proposed a method for greedily constructing sets with no 3-term arithmetic progressions. It is conjectured that there is a dichotomy between such sequences: those that have a periodic structure as the sequence satisfies…
The notion of an individual random sequence goes back to von Mises. We describe the evolution of this notion, especially the use of martingales (suggested by Ville), and the development of algorithmic information theory in 1960s and 1970s…
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…
We show how to enumerate words in $1^{m_1} \dots n^{m_n}$ that avoid the increasing consecutive pattern $12 \dots r$ for any $r \geq 2$. Our approach yields an $O(n^{s+1})$ algorithm to enumerate words in $1^s \dots n^s$, avoiding the…
Although the popular MNIST dataset [LeCun et al., 1994] is derived from the NIST database [Grother and Hanaoka, 1995], the precise processing steps for this derivation have been lost to time. We propose a reconstruction that is accurate…
Sequence organizations are viewed from two points: one is from informational redundancy or informational correlation (IC) and another is from k-mer frequency statistics. Two problems are investigated. The first is how the ICs exceed the…
The discriminator of an integer sequence s = (s(i))_{i >=0}, introduced by Arnold, Benkoski, and McCabe in 1985, is the map D_s(n) that sends n >= 1 to the least positive integer m such that the n numbers s(0), s(1), ..., s(n-1) are…
Developers across the world use autonumber or auto sequences field of the backend databases for developing both the desktop and web based data centric applications which is easier to use at the development and deployment purpose but can…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The…
Researches have been done on Ethiopic scripts. However studies excluded the Geez numbers from the studies because of different reasons. This paper presents offline handwritten and machine printed Geez number recognition using feed forward…
The absence of books and book chapters in the Web of Science Citation Indexes (SCI, SSCI and A&HCI) has always been considered an important flaw but the Thomson Reuters 'Book Citation Index' database was finally available in October of 2010…
The classic string indexing problem is to preprocess a string $S$ into a compact data structure that supports efficient subsequent pattern matching queries, that is, given a pattern string $P$, report all occurrences of $P$ within $S$. In…
The discriminator of an integer sequence s = (s(i))_{i>=0}, introduced by Arnold, Benkoski, and McCabe in 1985, is the function D_s(n) that sends n to the least integer m such that the numbers s(0), s(1), ..., s(n-1) are pairwise…
The Fibonacci numbers are familiar to all of us. They appear unexpectedly often in mathematics, so much there is an entire journal and a sequence of conferences dedicated to their study. However, there is also another sequence of numbers…
Novel dynamic programming algorithms to count the set $D(n)$ of zero-free degree sequences of length $n$, the set $D_c(n)$ of degree sequences of connected graphs on $n$ vertices and the set $D_b(n)$ of degree sequences of biconnected…
A large amount of information in today's world is now stored in knowledge bases. Named Entity Recognition (NER) is a process of extracting, disambiguation, and linking an entity from raw text to insightful and structured knowledge bases.…
The Houma Alliance Book, one of history's earliest calligraphic examples, was unearthed in the 1970s. These artifacts were meticulously organized, reproduced, and copied by the Shanxi Provincial Institute of Cultural Relics. However,…
This paper synthesizes the actions performed in order to transform a classic scientific research journal - 'Annals. Computer Science Series' - available only in printed form until 2008, into a modern e-journal with free access to the full…
A large-scale experiment was conducted to find formulas relating to the base $e^\pi$. The numbers in this base are $$x = \sum_{n=0}^\infty {a(n)\over e^{\pi n}}$$ where $a(n)$ is taken from the OEIS catalog. These experiments were inspired…
The rapid advance of DNA sequencing technologies has yielded databases of thousands of genomes. To search and index these databases effectively, it is important that we take advantage of the similarity between those genomes. Several authors…