Questions tagged [oeis]
For questions related to the On-Line Encyclopedia of Integer Sequences.
132
questions
2
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Proof of the remarkable formula for the n-th non-square?
The OEIS's A000037 entry makes the remarkable claim that every non-square number is given by the sequence $$a(n) = n + \Big\lfloor \frac 12 + \sqrt n\Big\rfloor$$ After looking through the entry, I ...
0
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1answer
32 views
On Hypergeometric Series and OEIS Sequence
I have been searching an integer sequence in OEIS. The sequence is the following: OEIS A321234 (https://oeis.org/A321234) . So far, so good. However, this sequence is the denominator of a ...
3
votes
0answers
26 views
Is there any website like OEIS for special polynomials
I would like to know if there is any kind of website (like OEIS) in which we can search for special known polynomials. For example, we put the coefficients of Legendre's and then the website gives us ...
1
vote
2answers
95 views
Explicit closed formulas for A056542 and A079751?
Consider the recurrence $B_1 = 0$, $B_n = nB_{n-1} + 1$ for $n\ge 1$ as defined by http://oeis.org/A056542 or by R. Sedgewick, Permutation generation methods, Computing Surveys, 9 (1977), 137–164. How ...
2
votes
1answer
68 views
Why this rational approximation $\pi\sim\frac{80249}{25544}$ is not mentioned in OEIS?
I have checked sequence of Denominator of best approximation to $\pi$ with denominator $\le10^n$ in OEIS but I didn't find this rational $\frac{80249}{25544}$ however it is better than $\frac{22}7$, ...
2
votes
1answer
127 views
Does a graded poset on $\mathbb{N}_{>0}$ generated from subtracting factors define a lattice?
Consider the partial ordering of positive integers with covering relations $n - \frac np \lessdot n$ for all prime divisors $p \mid n$. This defines a graded poset with $A064097$$(n)+ 1$ rank levels ...
9
votes
0answers
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Fractal Pattern from Queen's Move Construction
This question relates to the OEIS sequence A279212.
Fill an array by antidiagonals upwards; in the top left cell enter $a(0)=1$; thereafter, in the $n$-th cell, enter the sum of the entries of ...
17
votes
2answers
316 views
The equation $\sigma(n)=\sigma(n+1)$
In OEIS, the solutions of $$\sigma(n)=\sigma(n+1)$$ where $\sigma(n)$ denotes the sum of the divisors of $n$ including $1$ and $n$ , are shown upto $n=10^{13}$
The entry can be found already by ...
39
votes
0answers
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Is OEIS A248049 an integer sequence?
The OEIS sequence A248049 defined by
$$ a_n \!=\! (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.$$
is apparently an integer sequence but I ...
7
votes
1answer
52 views
Counting polysticks on the $n$-cube.
Over at Code Golf Stack Exchange, I put up a challenge asking people to count, among other things, the number of ways to take an $n$-cube and color $k$ (connected) edges up to isometries of the $n$-...
1
vote
0answers
36 views
Guises of the refined Eulerian numbers, generated by tangent vectors (OEIS A145271)
(Cross-posted from MathOverflow. See comments there for more background.)
The Eulerian numbers (OEIS A008292, not to be confused with the Euler numbers) pop up in numerous scenarios in combinatorics ...
0
votes
0answers
12 views
Examples of fusenes that are not polyhexes
OEIS sequence A108070 describes
Number of fusenes with n hexagons.
OEIS sequence A000228 describes
Number of hexagonal polyominoes with n cells.
These sequences first disagree at $A108070(7) =...
1
vote
2answers
80 views
About Harmonic Numbers and a sequence in OEIS
I'd been looking for a series in OEIS and the one that fits better (resembles, at least) is one in this link in Examples: http://oeis.org/A082687. There, as we can see, it is equal to
$$H'(2n) = H(...
0
votes
1answer
32 views
What is meant with “whose xor-sum is n”?
A sequence look-up led me to sequence A088512 in OEIS.org with description "Number of partitions of n into two parts whose xor-sum is n."
I know the "Number of partitions of n into two parts" which ...
1
vote
1answer
75 views
About $A_{n+1}=A_{n}+A_{n}^{2}$ and OEIS $A122888$
OEIS A122888 is: $1, 1, 1, 1, 2, 2, 1, 1, 3, 6, 9, 10, 8, 4, 1, 1, 4, 12, 30, 64, 118, 188, 258, 302, 298, 244, 162, 84, 32, 8, 1, 1, 5, 20, 70, 220, 630, 1656,\dots$
I'm having trouble ...
3
votes
1answer
47 views
Counting deltahedra with $2n$ faces
A deltahedron is, according to Wikipedia,
a polyhedron whose faces are all equilateral triangles.
There is only one deltahedron with four faces: the tetrahedron.
Likewise, there is only one ...
2
votes
1answer
47 views
Are the “distended” numbers precisely the numbers for which no two subsets of their divisors have the same sum?
The OEIS sequence A051772 defines the "distended" numbers as those positive integers $n$ for which each divisor of $n$ is greater than the sum of all smaller divisors.
Now, here's a question about ...
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0answers
34 views
How many of different connected graphs with n vertices? Excluding of isomorphic graphs.
Given $n$ vertices, the question is to answer how many different connected graphs exist?
For example, $f(1)=1,f(2)=1,f(3)=2,f(4)=6 \cdots$.
Here I exclude the isomorphic graphs.
I know there is a ...
2
votes
1answer
72 views
Number of strings of $\{0,1,2\}$ : the longest substrings of $1$ is odd-length.
Consider $A^* = \{0,1,2\}^*$. We want to know how many string of length $n$ in this alphabet following such property : all longest substrings of 1-s has odd length(let it be $a_n$).
I know that it ...
0
votes
2answers
83 views
Finding the next term in a sequence: $1,4,17,19,148,.?.$
Define $a(n)$ to be true if $n\mid(1^1+2^2+3^3+...+n^n)$
So $\{n\in\mathbb N\mid a(n)\}=\{1,4,17,19,148,...\}$
What is the sixth term?
I checked $1\le n\le 1000$, but did not find a sixth term.
...
2
votes
0answers
72 views
(Why) are $0, 1, 10, 120, 1540, 7140$ the only triangular tetrahedral numbers?
I recently came across entry A027568 of the OEIS, which reports the numbers
$$0, 1, 10, 120, 1540, 7140$$
as the set of integers which are both triangular and tetrahedral; that is, each can be written ...
1
vote
0answers
85 views
Are all positive odd integer matchs this three conditions will be a prime number?
The period length of the decimal expansion of $1/n = 2^x$ and $n-1$ divides by the length.
The sum of $n = 2^x$.
The cycle length of $n = 2^x$.
($x$ is some positive integer)
(using $n=23$ as an ...
4
votes
1answer
79 views
The pattern of $n$-th prime minus its reversal in even and odd bases
I recently saw the sequence A265326 on OEIS and also in Brady's Numberphile video Amazing Graphs ft. Neil Sloane
The sequence is such:
Start from $2$, given the
$x$-th prime number and convert it ...
3
votes
2answers
168 views
Computing Remy Sigrist sequence A279125
I am curious to understand how you can compute sequences like this one by Rémy Sigrist https://oeis.org/A279125
You can also see it in action in this numberphile video:
https://youtu.be/j0o-pMIR8uk?...
2
votes
2answers
83 views
Where to publish proofs for, for example, the OEIS
TL; DR; Where can I publish proofs that are not groundbreaking nor profound?
I recently found an integer sequence in the OEIS. Okay, the OEIS only contains integer sequences, so nothing new so far. ...
2
votes
1answer
74 views
What properties does the ratio of two triangular numbers $M$ and $N$ have, assuming $N \mid M$?
This is a follow-up question to this MSE post.
Call a number $X$ triangular if it could be written in the form $x(x+1)/2$ where $x$ is a positive integer.
Here is my question in this post:
What ...
0
votes
1answer
44 views
Is there a specific terminology for numbers which are nontrivial multiples of triangular numbers?
(Note: Please see this new question for the motivation.)
A number $T$ is said to be triangular if it could be written in the form
$$T=\frac{n(n+1)}{2},$$
where $n$ is a positive integer.
Here is my ...
7
votes
1answer
147 views
Binary weight of OEIS sequence A308092.
Preliminaries
OEIS sequence A308092 is defined as:
The sum of the first $n$ terms of the sequence is the concatenation of the first $n$ bits of the sequence read as binary, with $a(1) = 1$.
And ...
2
votes
1answer
173 views
Number of $n$-bead binary necklaces [OEIS-A000013]
I tried to obtain the number of $n$-bead binary necklaces from my program written in C++. Then, one formula came up when I looked up the number to see if my thought is correct.
Number of $n$-bead ...
0
votes
1answer
23 views
Intuitive geometric sequences (and where to find them in OEIS)
Wondering where intuitive "geometric sequences" are in OEIS. By intuitive, I mean things that you can easily describe to non-math people, as opposed to more obscure concepts that require some deeper ...
1
vote
1answer
21 views
Recurrence for A000670
A000670 contain a formula by Martin Kochanski:
Recurrence: $2a(n)=(a+1)^n$ where superscripts are converted to subscripts after binomial expansion - reminiscent of Bernoulli numbers $B_n=(B+1)^n$.
...
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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 ...
3
votes
1answer
31 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
49 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
83 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
45 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:
...
asked Dec 24 '18 at 9:44
Jose Arnaldo Bebita-Dris
7,9896 gold badges22 silver badges50 bronze badges
7
votes
0answers
134 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
46 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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vote
0answers
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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
169 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
46 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 ...
4
votes
1answer
758 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
1k 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 ...
17
votes
0answers
681 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
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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 prime number; otherwise equals to
$0$. I write $|A_n|$ to count the number of $1$'s in $A(n)$ and ...
1
vote
0answers
41 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
206 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
38 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
67 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
56 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 ...
