Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [oeis]

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

-3
votes
0answers
27 views

How we can use OEIS.org efficiently? [on hold]

My problem is that I don't how to use oeis.org searching problem relevant to some problems about combination, number-theory,geometry,...
0
votes
0answers
43 views

Crossing Number Graphs CN 9-13

At Crossing Number Graphs are minimal cubic graphs with crossing numbers 0 to 8. At Smallest Cubic Crossing Number Graph are some corrections -- 8D and 8E can be drawn with less than 8 crossings, and ...
2
votes
1answer
21 views

Number of unlabeled hypergraphs (A003180)

I'm looking for the number of unlabeled hypergraphs on n nodes and stumbled upon the comments of A003180 in OEIS. Can somebody please explain to me how that sequence relates to the number of unlabeled ...
4
votes
1answer
45 views

Why do these two sequences end in an increasing number of zeroes?

The trimorphic numbers are integers whose cubes end in the digits of the integers themselves, such as ${\sf{49}}^3=1176\sf{49}$, and I have discovered something interesting about such integers that ...
3
votes
1answer
49 views

Growth rate of primes vs. prime indexed primes

Looking at the graph of the prime indexed primes on oeis and the graph of the primes, it seems that the first graph has small jumps exactly at the same positions as the second. It's no surprise ...
4
votes
1answer
37 views

On an interesting assertion in the OeisWiki page on multiply-perfect numbers

The following (interesting) assertion appears in the OeisWiki page on multiply-perfect numbers: ...
7
votes
0answers
118 views

Gap in spiral sequence

OEIS sequence A272573 describes a sequence generated in the following way: Start a spiral of numbers on a hexagonal tiling, with the initial hexagon as a(1) = 1. a(n) is the smallest positive ...
2
votes
3answers
41 views

For $n,k \in {\mathbb{Z}}^{+}$ (excluding $n=1$), does $\frac{(n+k)!}{n!}$ ever equal $n!$

While investigating an integer sequence, I came across the following two OEIS entries: A094331: Least k such that n! < (n+1)(n+2)(n+3)...(n+k). A075357: a(n) = smallest k such that (n+1)(n+2)...(n+...
1
vote
0answers
29 views

Fewest number of distinct distances between $n$ points in $\mathbb Z^2$

I've been thinking about proving some bounds for the OEIS sequence A319476: $a(n)$ is the minimum number of distinct distances between $n$ non-attacking rooks on an $n \times n$ chessboard. I'd ...
1
vote
1answer
77 views

Lexicographically smallest sequence of integers not in the OEIS

A sequence $a_i$ ($i=1,\ldots$) is lexicographically smaller than sequence $b_i$ if either $a_1 < b_1$, or $a_j = b_j$ for $j=1,\ldots, k$ and $a_{k+1} < b_{k+1}$. If I asked for the ...
2
votes
1answer
33 views

Expected value of smallest element of descent set

I'm drafting an OEIS sequence, and I've formulated a few conjectures. I was hoping someone here could help me to prove them. Definition Let the descent set of a permutation $\omega \in S_n$ be the ...
2
votes
1answer
303 views

OEIS database download [closed]

I am interested in downloading the first 25 integers of each sequence in the OEIS database. My reason for wanting to do so is to find the arithmetic mean of the first integers, the arithmetic mean of ...
13
votes
4answers
930 views

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 ...
15
votes
0answers
628 views

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 ...
1
vote
0answers
44 views

The numbers $n$ such that every sum of consecutive positive numbers ending in $n$ is not prime or A138666?

Question: Let $A(n)$ be a finite square $n \times n$ matrix with entries $a_{ij}=1$ if $i+j$ is a perfect power; otherwise equals to $0$. I write $|A_n|$ to count the number of $1$'s in $A(n)$ and ...
1
vote
0answers
32 views

Reducing a system of Linear Recurrences

The number of ways to lay unit-length matchsticks on a $2 \times n$ grid (with respect to vertices) appears to be given by OEIS sequence A093129, but I found it a different way, and I'm looking for ...
5
votes
2answers
176 views

Explanation for OEIS $\text{A}000157$ – “Number of Boolean functions of $n$ variables”

I'm having trouble understanding OEIS $\text{A}000157$, not necessarily its description, but rather its terms. I've already visited how many semantically different boolean functions are there for n ...
5
votes
1answer
35 views

On a certain OEIS convention

Do you know what it is that those numbers which appear in the upper-right angle of the blue-box mean? I presume they have to do with a certain ranking of the sequences within the site, but I am not ...
1
vote
1answer
54 views

Two miscellaneous questions about equations involving the Euler's totient function and twin primes

This morning I was thinking in equations involving the Euler's totient function $\varphi(n)$ and the sequence of twin primes (see if you want this MathWorld). I am saying similar questions than ...
3
votes
0answers
53 views

Group notation in OEIS

I am wondering how I should interpret the notation that the Online Encyclopedia of Integer Sequences (OEIS) uses for finite groups. An example is this sequence: A008795 In this specific case, what ...
3
votes
1answer
185 views

Counting particular odd-length strings over a two letter alphabet.

OEIS sequence A297789 describes The number of [equivalence classes of] length $2n - 1$ strings over the alphabet $\{0, 1\}$ such that the first half of any initial odd-length substring is a ...
10
votes
1answer
676 views

Sufficiently large integers can be partitioned into squares of distinct integers whose reciprocals sum to 1.

OEIS sequence A297895 describes Numbers that can be partitioned into squares of distinct integers whose reciprocals sum to 1. ...
2
votes
1answer
283 views

Properties of triangles with integer sides and area

OEIS sequence A051518 describes There exists a triangle of perimeter $n$ having integer sides and area. And begins ...
14
votes
1answer
511 views

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 ...
2
votes
0answers
139 views

Counting Semistandard Young Tableaux For Triangular Shapes?

If $k \leq n$ I denote the Young diagram with shape $(n,n-1,n-2,\ldots,1)$ by $\lambda^{n,n-1,\ldots,1}$. I write $f^{\lambda_n^{n,n-1,\ldots,1}}$ to count the number of semistandard Young tableaux ...
12
votes
0answers
2k views

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 ...
7
votes
0answers
166 views

Magic Cubic Curve Permutations

The permutation $(-2,9,-4,7,-6,5,-8,3,1)$ can be considered magical. With their negative values diametrical to $0$ at $(0,0)$, a placement of integers begins so that all zero-sum triples form straight ...
8
votes
1answer
239 views

Removing points from a triangular array without losing information

I'm trying to find insights about the following puzzle, to see if I can find it on the OEIS (and add it if it's not already there): Suppose I give you a triangular array of light bulbs with side ...
2
votes
3answers
103 views

Add an edge to a graph without becoming nonplanar

This is an attempt to generate numbers in the sequence A000109, where efficiency is not necessary (Yes, this is yet another help question for the OEIS sequences :P) One of the methods of calculating ...
4
votes
0answers
58 views

Treasures from the OEIS Plot 2

The On-Line Encyclopedia of Integer Sequences provide us a tool with the link Plot 2. With this tool one can perform comparisons between two different sequences of positive integers. In number theory ...
-2
votes
1answer
52 views

Is these sequence present on OEIS? [closed]

Sequence one Number which is equal to the product of the factorials of its digits. Sequence two Factorial of a number is equal to the product of factorials of its digits.
2
votes
1answer
27 views

Minimal number of supporters need to win a multi-level election

On July 27th, Max Alekseyev posted a sequence to the OEIS: A290323: Minimal number of supporters among total of n voters that may make (but not guarantee) their candidate win in a multi-level ...
1
vote
1answer
89 views

Euler Transform between A000335 and A000292

The explanation for OEIS:A000335 states: Euler transform of A000292 where A000292 is the tetrahedral numbers. According to MathWorld: There are (at least) three types of Euler transforms (or ...
1
vote
1answer
123 views

Series-Parallel Numbers: Explanation for OEIS A000137

The sequence A000137: 1, 2, 6, 18, 58, 186, 614, 2034, 6818, 22970, 77858, 264970, 905294, 3102434, ... only has the following description on OEIS: Series-...
9
votes
2answers
320 views

Explanation of OEIS:A000236 - Residue Classes

I'm looking at OEIS:A000236, whose definition states: Maximum m such that there are no two adjacent elements belonging to the same n-th power residue class modulo some prime p in the sequence 1,2,.....
5
votes
1answer
65 views

Explanation of OEIS:A000046

I'm looking at OEIS:A000046, whose definition states: Number of primitive n-bead necklaces (turning over is allowed) where complements are equivalent. I can't quite understand this. This is what I ...
2
votes
1answer
135 views

Proof of minor claim related to the Twin Primes Conjecture

Question: How can it be proven that integers of the form $n=6jk\pm j \pm k;\ j,k\in \mathbb N^*,$ are the only ones which (when multiplied by $6$) correspond to multiples of $6$ not between twin ...
4
votes
0answers
181 views

Whats the next number in OEIS A258107? (PART I of II)

Part II is here OEIS LINK I've watched Dr James Grimes explain Why 82,000 is an extraordinary number. I was intrigued by this sequence and disocvered the following patterns. I was wondering if I ...
1
vote
1answer
95 views

The minimum “height” of a convex polygon on $\mathbb{N}^2$.

I've defined a new OEIS sequence but I'm having trouble figuring out a reasonable way to compute more terms. A285521: Table read by rows: the $n$-th row gives the lexicographically earliest ...
6
votes
0answers
214 views

The number of distinct least prime factors in a sequence of consecutive integers

I was thinking about the number of distinct least prime factors in a sequence of consecutive integers and I noticed: That every $4$ integers, there are $3$ distinct least prime factors. Every $6$ ...
9
votes
5answers
488 views

What is the $m$th derivative of $\log\left(1+\sum\limits_{k=1}^N n_kx^k\right)$ at $x=0$?

Let $n_k$ be integers. Is there a general formula for the Taylor expansion of $\log(1+\sum_{k=1}^N n_kx^k)$ at $x=0$? This boils down to find an expression for the $m$th derivative of $\log(1+\sum_{k=...
2
votes
2answers
44 views

How to interpret this comment from OEIS A050229?

I've been wracking my brain trying to gleam some insight into this comment from 2007: Numbers n for which there is a permutation of 0..n-1 such that each number is the sum of all the previous, plus ...
1
vote
1answer
33 views

Polynomials $P(x,y)$ with nonnegative integer coefficients such that $P(x,y) \equiv 1 \text{ (mod } x+y-1)$ and $P(1,1) = n$.

In 1971 Richard Guy sent a letter to Neil Sloane outlining some integer sequences. One of these sequences, A279196, was added to the OEIS by Neil only in December of 2016: A279196: Number of ...
0
votes
1answer
70 views

Link of a power series by the Bernoullis for a Riccati equation to zonotopes?

On pg. 85 of The Rise and Development of Theory of Series up to the Early 1820s by Ferraro is a series soln. of $$ d^2z/z = -x^2dx^2 $$ related to the reputed first appearance of a Riccati-type eqn.,...
0
votes
1answer
48 views

Lexicographically earliest sequence such that no subset sums to a prime.

OEIS sequence A052349 is given by: Lexicographically earliest sequence such that no subset sums to a prime. 1, 8, 24, 25, 86, 1260, 1890, 14136, 197400, 10467660, 1231572090, 682616834970 I ...
8
votes
0answers
123 views

Minimum number of terms of strictly increasing minimal sequence whose product is square.

Ron Graham's sequence is a neat bijection from the positive integers to the non-primes, defined as following: $a(n)$ = smallest $m$ for which there is a sequence $n = b_1 < b_2 < \dotsc < ...
8
votes
1answer
80 views

Asymptotic Growth of A279688: Numbers n such n and 2n are anagrams in some base.

I'm perplexed by the growth behavior of my recent OEIS Sequence A279688: Numbers $n$ such $n$ and $2n$ are anagrams in some base. Some examples of this sequence: $a(2) = 8$ because in base 5, $...
2
votes
1answer
94 views

The least common multiple of $n-2$ and $n+2$

Let $n$ be a positive integer greater than zero. Let $a_n= {n(n+3)(n-1) \above 1.5pt 2}$ and set $$\rho_n = {a_n \above 1.5pt gcd(n, a_n)}$$ Computation show that $\rho_n$ is the sequence $$0,5,6,21,...
3
votes
2answers
136 views

What is the asymptotic density of deficient-perfect numbers?

Let $\sigma(n)$ denote the sum of the divisors of the natural number $n$. Denote the deficiency of $n$ as $D(n) = 2n - \sigma(n)$. Here is my question: What is the asymptotic density of natural ...
3
votes
3answers
122 views

The $n^{th}$ digits of $e+\pi$ and a periodic sequence

Let $n$ be a positive integer greater than zero. I denote the $n^{th}$ digits of $e$ and $\pi$ by $e_n$ and $\pi_n$ respectively. Let $d(e_n+\pi_n)$ count the number of divisors of $e_n+\pi_n$ and set ...