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Questions tagged [oeis]

For questions related to the On-Line Encyclopedia of Integer Sequences.

The On-Line Encyclopedia of Integer Sequences, also called OEIS, is an online database of integer sequences, founded in 1964 by N.J.A. Sloane, and maintained by the OEIS Foundation.

It currently (August 2022) contains over 356,000 integer sequences.

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Mondrian Art Problem Upper Bound for defect

Divide a square of side $n$ into any number of non-congruent rectangles. If all the sides are integers, what is the smallest possible difference in area between the largest and smallest rectangles? This is known as the Mondrian Art Problem. For…
Ed Pegg
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Is $a_0=2$, $a_1=a_2=a_3=1$, $a_n=\frac{(a_{n-1}+a_{n-2})(a_{n-2}+a_{n-3})}{a_{n-4}}$ (OEIS A248049) an integer sequence?

The OEIS sequence A248049 defined by $$ a_n \!=\! \frac{(a_{n-1}\!+\!a_{n-2})(a_{n-2}\!+\!a_{n-3})}{a_{n-4}} \;\text{with }\; a_0\!=\!2, a_1\!=\!a_2\!=\!a_3\!=\!1 $$ is apparently an integer sequence but I have no proofs. I have numerical evidence…
Somos
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Repeatedly taking mean values of non-empty subsets of a set: $2,\,3,\,5,\,15,\,875,\,...$

Consider the following iterative process. We start with a 2-element set $S_0=\{0,1\}$. At $n^{\text{th}}$ step $(n\ge1)$ we take all non-empty subsets of $S_{n-1}$, then for each subset compute the arithmetic mean of its elements, and collect the…
Vladimir Reshetnikov
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A sequence of coefficients of $x+(x+(x+(x+(x+(x+\dots)^6)^5)^4)^3)^2$

Let's consider a function (or a way to obtain a formal power series): $$f(x)=x+(x+(x+(x+(x+(x+\dots)^6)^5)^4)^3)^2$$ Where $\dots$ is replaced by an infinite sequence of nested brackets raised to $n$th power. The function is defined as the limit…
Yuriy S
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How many "prime" rectangle tilings are there?

Given two tilings of a rectangle by other rectangles, say that they are equivalent if there is a bijection from the edges, vertices, and faces of the tilings which preserves inclusion. For instance, the following two tilings are equivalent (some…
RavenclawPrefect
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Enumerating all fractions by $x \mapsto x +1$ and $x \mapsto-\frac1x$.

In January 2022, MathOverflow user pregunton commented that it is possible to enumerate all rational numbers using iterated maps of the form $f(x) = x+1$ or $\displaystyle g(x) = -\frac 1x$, starting from $0$. Let $X_n$ be the rational numbers can…
Peter Kagey
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Greatest number of non-attacking moves that queens can make on an $n \times n$ chess board.

I'm trying to extend my OEIS sequence A275815: Maximum total number of possible moves that any number of queens of the same color can make on an $n \times n$ chessboard. I have computed the first five terms by brute force, and examples of each are…
Peter Kagey
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How many lattices does it take to cover a regular $n$-gon?

Given some positive integer $n\ge 3$, we can ask how many 2-dimensional lattices $L_1,\ldots,L_k$ are required such that their disjoint union contains all vertices of a regular $n$-gon. (We don't require that the lattices be centered at the…
RavenclawPrefect
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Smallest region that can contain all free $n$-ominoes.

A nine-cell region is the smallest subset of the plane that can contain all twelve free pentominoes, as illustrated below. (A free polyomino is one that can be rotated and flipped.) A twelve-cell region is the smallest subset of the plane the can…
Peter Kagey
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Is Conway's "Look and Say Sequence" strictly increasing?

I have a straightforward question about Conway's "Look and Say Sequence (A005150): The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. Starting with 1, the sequence would be defined…
Brendan W. Sullivan
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The equation $\sigma(n)=\sigma(n+1)$

In OEIS A002961, the solutions of $$\sigma(n)=\sigma(n+1)$$ where $\sigma(n)$ denotes the sum of the divisors of $n$ including $1$ and $n$, are shown up to $n=10^{13}$ The entry can be found already by entering the first three solutions…
Peter
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How many combinatorially distinct ways are there to tile an equilateral triangle with $k$ $60^\circ-120^\circ$ trapezoids?

I believe there is exactly one way (up to combinatorial equivalence) to arrange 3 trapezoids with angles of $60^\circ$ and $120^\circ$ into an equilateral triangle: With $4$ trapezoids, I see two ways: With $5$ trapezoids, there are many more; I…
RavenclawPrefect
  • 18,328
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4 answers

Why would you take the logarithmic derivative of a generating function?

Today, my climbing expedition scaled Mt. Sloane to request the Oracle's Extensive Insight into Sequences. The monks there had never heard of our plight, so they inscribed our query in mystical runes on a scrip of paper and took it into a room we…
algorithmshark
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Does the "prime ant" ever backtrack?

A few mathematical questions have come up from the question "The prime ant " on the Programming Puzzles & Code Golf Stack Exchange. Here is how the prime ant is defined: Initially, we have an infinite array A containing all the integers >= 2 :…
Peter Kagey
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A generalization of the product of harmonic numbers to non-integer arguments

This question is somewhat related to one of my previous questions: Fibonorial of a fractional or complex argument. Recall the definition of harmonic numbers: $$H_n=\sum_{k=1}^n\frac1k=1+\frac12+\,...\,+\frac1n\tag1$$ Obviously, harmonic numbers…
Vladimir Reshetnikov
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