# Questions tagged [oeis]

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

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### Counting endofunctions by inclusion–exclusion

While leafing through the OEIS, I noticed the following conjecture (from Werner Schulte, OEIS A000312 ): For integer $n \ge 0$ $$\sum_{k=0}^n (-1)^{n - k} { n \brack k }{n+k \brace k} = n^n .$$ ...
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### Is there really no way to generate infinitely many primes?

Is there really no way to generate infinitely many primes? A previous answer for someone asking about the Infinite generation of primes, says: There is no exact way to generate primes continuously. ...
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### Counting permutations $\pi \in S_n$ such that $\pi(i) \neq i$ and $\pi(i) - k \not\equiv i \bmod n$.

Given integers $n > 2$ and $1 \leq k < n$, I'm interested in the set of permutations $$\{\pi \in S_n : \pi(i) \neq i \text{ and } \pi(i) - k \not\equiv i \bmod n\}.$$ When $k = 1$, these are ...
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### Asymptotic for $\sum_{k=1}^n k^n$

Consider the OEIS sequence A031971, which is defined as: $$a_n=\sum\limits_{k=1}^n k^n\quad\color{gray}{(1,\,5,\,36,\,354,\,4425,\,67171,\,1200304,\,.\!.\!.\!)}\tag{1}$$ I'm interested in the ...
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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 ...
1 vote
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### Question about the least prime $p$ such that $p+2n$ is also prime.

In the sequence Least prime $p$ such that $p+2n$ is also prime page (A020483) on OEIS, it says: If $a(n)$ exists, $a(n) < 2n$ What does it mean? At first it sounds like if both $p$ and $2n+p$ are ...
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### Pattern in number of digits in $(10^n)!$

I was observing the OEIS sequence A061010 and its values up to $n=1000$, and it seems that the pattern is as follows. For $n$, $f(n)$ is for the form string of $(n-1)$+(pattern of repeating digits ...
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### An analogue to OEIS for graphs and ordered pairs?

Does anyone know if such a thing exists already? I was able to find a number of seemingly very comprehensive encyclopedia-like reference pages on many species of graphs, but it seemed that the use ...
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### Lyndon words over the binary alphabet that begin with "00"

Lydon words over the binary alphabet are strings of $1$s and $0$s such that all rotations of the word are strictly lexicographically later. I've been looking at Lyndon words of length $n$, which are ...
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### Understanding first hitting time probabilities for a $2d$ random walk

The probability for a random walk that starts at the origin to return to the origin for the first time after exactly $2n$ steps has been solved on this site a couple times for the $1$d random walk. ...
1 vote
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### Probability distribution of number of returns after $2n$ steps of $1d$ random walk

The expected number of returns of a simple random walk in $1d$ after $2n$ steps is a well known problem, with answer $\sum_{m=1}^n \frac{\binom{2m}{m}}{2^{2m}}$. A question that requires more ...
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### OEIS A333017, or something else entirely?

I am trying to find out how to calculate the number of different relationships there are between all the non-empty cliques that can be made of a given number 'n' of individuals. Doing this manually (...
1 vote
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### Regarding OEIS and integer sequences

The OEIS, aka Sloane, is an online repository of over $3,20,000$ integer sequences. Now, suppose I have an integer sequence, say, $a_1, a_2, a_3, ...$ I look for this sequence in OEIS. The sequence ...
1 vote
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### Does replacing each prime factor of an odd abundant number with the preceding prime always give another abundant number?

Given an odd abundant number $n$, if one replaces each prime factor of $n$ with the preceding prime while maintaining the same multiplicity (which gives A064989($n$)), does one always get another ...
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### Generation function for the finite Coxeter group of type $D_k$

Basically I'd like to know how to derive the generation function for the finite Coxeter group of type $D_k$ to be familiar with notes in OEIS A162288: According to formula section: 'The growth series ...
1 vote
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### Question about A051002 in OEIS

I have a question about sequence https://oeis.org/A051002 in the OEIS database with first elements 1, 1, 244, 1, 3126, 244. I searched however for ...
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### A recursive approach to Josephus problem (OEIS 225381)

Taking integer $x$ as input: If $x$ is even, then return $x/2$ as series item, giving $x/2$ as input to continue the loop; Else return ceiling($x/2$) as series item, terminate the loop; Finally we sum ...
1 vote
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### Series $\sum_{k=0}^\infty \frac{k^u}{k!}$---something known? [duplicate]

Define $f(u)=\sum_{k=0}^\infty \frac{k^u}{k!}$ for natural numbers $u$. Using maple I can find the sum for specific values of $u$, but there is no general answer (unsurprisingly). All values I found ...
1 vote
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### Non-values of $a^3 + b^{c^3} - 3 a b c$ for $a,b,c\in\mathbb{N}$ like $n$ for prime $19n+17$?

I stumbled on a curious case of Richard Guy's Strong Law of Small Numbers because of a typographical error. I intended to type a^3 + b^3 + c^3 - 3 a b c and look at ...
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### Are (1,2) and (4,5) the only two consecutive pairs in A003592?

All odd numbers in A003592 are powers of $5$, so this is equivalent to finding all $n \ge 0$ such that $5^n = 2^m+1$ or $2^m - 1$ for some $m \ge 0$. By quick brute force computation I cannot seem to ...
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### Number of convex polyhedra whose faces are regular polygons and whose largest face is an $n$-gon

I'm trying to count up the number of convex polyhedra whose faces are regular polygons and whose largest face is an $n$-gon. (I.e. either a uniform polyhedron or a Johnson solid.) If I've done my ...
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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 ...
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### 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 ...
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### 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
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 ... 