Questions tagged [oeis]
For questions related to the On-Line Encyclopedia of Integer Sequences.
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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,...
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0answers
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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
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1answer
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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
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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
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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
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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
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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
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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+...
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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
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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
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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
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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
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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 ...
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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 ...
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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
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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
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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 ...
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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
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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 ...
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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.
...
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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
...
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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
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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 ...
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0answers
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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 ...
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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
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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
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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
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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 ...
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1answer
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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.
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1answer
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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
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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 ...
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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-...
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2answers
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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
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1answer
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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
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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 ...
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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
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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 ...
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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 $6$ ...
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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=...
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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 ...
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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 ...
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1answer
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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
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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 ...
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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
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1answer
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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
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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,...
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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 ...
