Related papers: On Two OEIS Conjectures
A serial property is a suitably enumerated sequence $\{F_n\}$ of formulas and is called selector provable in PA if there is a PA-recursive function $s(x)$ such that PA $\vdash \forall x (s(x){:}_{\text{PA}} \ulcorner F_x\urcorner)$ where…
This experimental study presents some interesting conjectured relations between some integer sequences and certain graph parameters of the family of linear Jaco graphs $J_n(x)$ where $n = 1,2,3,\dots$. It appears that $\textit{Golden…
In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and reformulated here, the second moment of the distribution of the…
In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture…
We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.
We prove generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns. Our main tool is the perhaps surprising observation that a classic bijection on pattern avoiding…
This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…
We prove a series of Stephan's conjectures concerning Pascal triangle modulo 2 and give a polynomial generalization.
For the OEIS sequence A032123, the number of length-$2n$ black-and-white strings with $n$ black beads, considered up to reversal, R. J. Mathar contributed in November 2013 the conjectured order-5 P-recursive recurrence \[ \begin{aligned}…
In a recent work, Andrews gave analytic proofs of two conjectures concerning some variations of two combinatorial identities between partitions of a positive integer into odd parts and partitions into distinct parts discovered by Beck.…
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.
Euler evaluates the integrals in the title and recognizes a recursion between them, which he then uses to give continued fractions for the log and arctan. The paper is translated from Euler's Latin original into German.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
The conjecture of Masser-Oesterl\'e, popularly known as $abc$-conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures.
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
The Scholz conjecture on addition chains states that $\ell(2^n-1) \leq \ell(n) + n -1$ for all integers $n$ where $\ell(n)$ stands for the minimal length of all addition chains for $n$. It is proven to hold for infinite sets of integers. In…
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…
Rosenfeld in 1974 conjectured that there is an integer N > 8 such that every tournament of order n > N contains every non-directed cycle of order n. We prove that, with exactly 35 exceptions, every tournament of order n > 2 contains each…