Questions tagged [oeis]
For questions related to the On-Line Encyclopedia of Integer Sequences.
211 questions
26
votes
1
answer
534
views
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
2
votes
0
answers
37
views
Kolakoski sequence $K(1,3)$ recursive $K(1,2)$ not...
Why does the Kolakoski sequence $K(1,3)$ admit a precise recursive block-pillar structure where
$$B_{n+1} = G(B_n, 1) = B_n \cdot P_n \cdot B_n$$
when no such simple construction exists for $K(1,2)$?
...
3
votes
1
answer
92
views
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 ...
- 21.9k
1
vote
1
answer
73
views
What convergence test to use for $\sum( 1/ P_n)$ where $P_n$ is the maximal prime gap primes?
I know that $1/p_k$ diverges slowly. https://en.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocals_of_the_primes
This sequence is different. By choosing only to sum the ends of the maximal ...
- 508
1
vote
1
answer
54
views
Number of labeled Eulerian digraphs with 3 nodes
In OEIS A007080 it says the number of labeled Eulerian digraphs with 3 nodes is 10. I struggle to find the 10 possibilities. I find only six: 1-2-3-1, 1-3-2-1, 2-1-3-2, 2-3-1-2, 3-1-2-3 and 3-2-1-3. ...
- 614
4
votes
0
answers
64
views
Integers $k$ where $\sin k$ (in radians) increases monotonically to 1
A046959 describes integers $k$ where $\sin k$ (in radians) increases monotonically to 1. The first few terms of this sequence $a_n$ are $0,1,2,3,8,14,33$, and the sines of these values are:
$$\begin{...
- 71
2
votes
1
answer
66
views
Three non-isomorphic rings whose additive group is the Klein four-group.
I was looking at OEIS sequence A037291, which gives the number of rings with identity that have $n$ elements. That page linked me to a website written by C. Noebauer which claims that there are three ...
- 5,438
1
vote
2
answers
63
views
Issue with Calculating Terms of OEIS Sequence A187278 Using SageMath
I’m trying to compute the terms of the OEIS sequence $A187278$ using SageMath. This sequence, described as "The radical part of the expression whose continued fraction has periodic part $1, 2, \...
1
vote
1
answer
189
views
Could someone provide an analytical proof of empirically found formula?
$$a(n) = 2^{n/2 - 2} \times [(2 \sqrt 2 - 3) \times (-1)^{n + 1} + 3 + 2
\sqrt 2)] + 2$$
Above empirically found concurrent formula matches OEIS sequence A209722, This sequence counts a specific ...
- 103
0
votes
2
answers
204
views
On the OEIS sequence A346789
I have a question about the sequence A346789. It states the following:
Given any sufficiently large number $k$, the smallest number having
$k$ as the sum of the cubes of its digits is the ...
- 11
3
votes
0
answers
133
views
How can I prove that $3(\sum_{i=1}^{n}{\lfloor \frac{i^2}{n} \rfloor}) - n^2 \geq 2\ $ for all $n\geq 2?$
The OEIS sequence A175908 represents a sequence derived from this formula:
Using the Legendre $\operatorname{L}$-Function, I was able to prove that
for primes $n$ of the form $4k + 1$, the value ...
- 51
4
votes
2
answers
580
views
Increasing vs non decreasing
In this video (at this timestamp) Neil Sloane says that the function is increasing, then corrects himself and says "I should say non-decreasing". To me, those both sound the same. Obviously ...
- 143
3
votes
1
answer
123
views
Are there any primes that satisfy the third iteration of this process?
OEIS sequence $\text{A}092738$ lists primes that can be represented as the sum of two consecutive primes, plus $1$. This process can be iterated; if we call these numbers "sprimes" (summed ...
- 1,797
0
votes
1
answer
76
views
What is a connected function with a fixed point in A000081
Very short question, which I ask because the ressources on Oeis did not help:
What is meant by a connected function with fix point on https://oeis.org/A000081 ?
Maybe I missed something but I do not ...
- 1,373
0
votes
1
answer
57
views
Asymptotic behaviour of number of isomeric $n-$ alkanes
I wonder about the asymptotic behaviour of the integer sequence discussed in this question. As answered there OEIS has the sequence on hand, and the linearlity of logarithmic scatterplot there ...
- 5