Questions tagged [oeis]
For questions related to the On-Line Encyclopedia of Integer Sequences.
222 questions
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A similar sequence to OEIS-A098021
Let $U_0=0$, we make $U_n$ by the following rules :
If $\color{magenta}n=U_k$ for some $k \in \mathbb{N}$ ,
$$U_{n+1} = U_{\color{magenta}n} + \color{red}5$$
$$U_{n+2} = U_{n+1} + \color{red}5$$
...
- 604
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A new prime-indexed additive sequence and its properties
I would like to share and ask about the following integer sequence that I have been experimenting with, while looking for “simple but rich” sequences in the spirit of OEIS contributions.
I start from $...
- 3,054
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Integer coefficients defined recursively with main diagonal equals A195979
Let
$A_n(x)$ be the family of exponential generating fucntions such that $$ A'_n(x) = nA_n(x) + A_{n-1}(x), \\ A_n(0) = 1, A_0(x) = 1. $$
$T(n,k)$ be an integer coefficients whose exponential ...
user929945
2
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1
answer
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Closed form for A375540
Let
$a(n)$ be A375540, i.e., an integer sequence such that $$ a(n) = n! [x^n] (2e^x-1)^n. $$ Note that here $(2e^x-1)^n$ is an exponential generating function, and $[x^n]$ is a coefficient of ...
user929945
1
vote
1
answer
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Recursion for row polynomials of A083906
Let
$T(n,k)$ be A083906, i.e., an integer coefficients such that $$ T(n,k) = [q^k] \sum\limits_{m=0}^{n} \binom{n}{m}_q. $$ Here $\binom{n}{m}_q$ is a Gaussian $q$-binomial coefficients.
$R(n,k)$ be ...
user929945
6
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1
answer
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Fast and simple recursive algorithm for A375540
Let
$a(n)$ be A375540, i.e., an integer sequence such that $$ a(n) = 2^n n! [x^n] (1/2 - \exp(-x))^n. $$
Start with vector $\nu$ of fixed length $m$ with elements $\nu_i = 1$ (that is, $\nu = \{1,1,\...
user929945
3
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1
answer
107
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Is the number of n-bead necklace structures using exactly seven different colored beads given by 7th column of A152175?
Question: Is the number of n-bead necklace structures using exactly seven different coloured beads given by the seventh column of OEIS A152175 "Triangle read by rows: T(n,k) is the number of k-...
3
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0
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64
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Intersections of diagonals inside and outside a row of squares
Consider a row of $n$ congruent squares. Draw a line through each pair of vertices. Find the number of intersections (without multiplicity) strictly inside this row of squares, $A_n$, and the total ...
- 3,770
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Explanation of sequence of partitions into four groups
Can someone explain definition of sequence A340761 (https://oeis.org/A340761) from OEIS and provide example?
Let's call this sequence $a(n)$. I know what integer partition (in this case I would ...
0
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2
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158
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Let n be a composite number greater than 6. Is the sum of n's prime factors less than n?
This is a lemma needed for How quickly does the sum of prime factors chain grow?
Let $n \in \mathbb{N}, n > 6$. Define $$factors(n)$$ as all prime factors of n, including 1, with multiplicity. So:
<...
- 438
5
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1
answer
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How quickly does the sum of prime factors chain grow?
Consider the sequence defined as follows:
Start with a number N. Compute the prime factors of N with multiplicity, and add 1. Then, sum this list together to get N'. Iterate this procedure until you ...
- 438
2
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0
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98
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Does Ruzsa's theorem imply a stronger lower bound than $\sqrt{n}$ for OEIS sequence A030193?
My question is based on an existing result of Ruzsa: Difference sets without squares
I noticed that on OEIS A030193, the sequence is said to be at least proportional to $\sqrt{n}$. But in the result ...
- 179
0
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0
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44
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An observation about the number of transitive relations.
I know that there is not a closed-form formula that counts all transitive relations on an $n$-set.
Let $t_n$ be the number of transitive relations on an $n$-set.
From the available values of $t_n$ in ...
- 3,613
26
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1
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709
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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 ...
- 5,438
3
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1
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For $\{-1,0,1\}$ polynomials, which have a higher early prime density than $x^2 + x - 1$?
Back in 1929, L. Poletti noticed $x^2 + x - 1$ generated a high density of primes A045548, with 49 primes in the run 1 to 100. I took a look at $\{-1,0,1\}$ polynomials up to order 8, looking to see ...
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