Questions tagged [pattern-recognition]

1. From a samples of a small samples of mathematical objects, conjecture a common pattern to all of them. This includes "guess the next terms in the sequence" question (consider checking OEIS first). Please provide as much context as possible. 2. Mathematical ideas related to pattern recognition, subfields of AI and statistics. Please check first if StackOverflow, Computer Science Stack Exchange, or Cross Validated is more appropriate.

Filter by
Sorted by
Tagged with
1 vote
1 answer
62 views

Extracting formula by pattern of child's game

Imagine there is a series of letters (a ,b , c): a1+b1+c1+a2+a2+b2+b2+c2+c2+a3+a3+a3+b3+b3+b3+c3+c3+c3+... And we will divide it in group of N, then need to determine the value of [P,Q] where P ...
Turtle1606's user avatar
5 votes
1 answer
113 views

Number of Salem–Spencer subsets of $\{1,2,3,\dots ,n\}$

I was wondering about sets that do not contain any $3$-term AP, and came to know that the official name of such a set is Salem–Spencer set. I was considering the question of counting the number of ...
Sayan Dutta's user avatar
  • 8,641
0 votes
0 answers
29 views

pattern for finding neghboring sub squares in a grid.

I am a programmer working on some code, and I think I found a good way to solve a programming issue, but I'm too weak in math, so I need your help: I have a grid, where I need to find all the opposing ...
Daniel Bengtsson's user avatar
3 votes
0 answers
84 views

On thickness of binary polynomials

OEIS A169945 introduces the concept of thickness of a polynomial as the magnitude of the largest coefficient in the expansion of the square of the polynomial. Considering the $2^{n+1}$ polynomials $p(...
Sayan Dutta's user avatar
  • 8,641
0 votes
0 answers
12 views

Using graphs to quantify the structure/pattern or correlation among the elements of supposedly random matrix

Let's say I have a supposedly random real symmetric matrix. How to use graphs to quantitatively (with a numerical focus) examine any structure/pattern or correlation among its elements ?
Snpr_Physics's user avatar
0 votes
1 answer
33 views

Pattern of hexagonal matches

I have a question about close form formula of this pattern. As you see the first one has $a(1)=6$ matches,$a(2)=24$and $a(3)=48$ The question ask for $a(10)$ , I found the number of matches as below $$...
Khosrotash's user avatar
  • 24.7k
4 votes
1 answer
220 views

What is this boolean pattern?

I am trying to come up with an invertable 1 or 2 dimensional transformation that is not unlike the fast fourier transform. Given a prior sequence $A_0 .. A_{n-1}$, we can generate a new sequence of ...
micsthepick's user avatar
3 votes
0 answers
69 views

Linear clustering when plotting Pisano periods

Recently I saw a video on YouTube where the Fibonacci numbers were studied and around minute 4:20 appears a graph showing the period against the modulus. Something that caught my attention is that ...
Amahury Diaz's user avatar
5 votes
1 answer
117 views

AMC Question 28 2021 SEN

I am studying for the AMC and I am stuck on a question and do not understand the solution to it. Both the question and solution are attached. What I am unsure about the solution is: when it says that ...
mathisdagoat's user avatar
0 votes
1 answer
25 views

Recommendation of Dispense Amount Based on Historical Averages [closed]

I am working on creating a function to provide recommendations for the amount to dispense. I have historical data on the average daily dispense amount for each item, but I lack information on the ...
feter's user avatar
  • 13
1 vote
1 answer
85 views

What is the pattern so we can make the next stars?

I found the following pattern question in a group! It took me a lot of time but unfortunately I don't have any ideas to find any logical thing here. Here's the picture of the question: The question ...
Amirreza Hashemi's user avatar
0 votes
0 answers
155 views

Pattern recognition Questions

To begin with, I do not know whether this community is the appropriate place to ask this type of question and if it violate the purpose of the community, I beg to apologise. I am preparing for an exam ...
asdsad's user avatar
  • 1
0 votes
1 answer
49 views

Struve function: simplify $\mathrm{H}_n(x) - (-1)^n \mathrm{H}_{-n}(x)$ for $n=1,2,3,...$

Consider this expression: $$A_n(x) =\frac{\pi}{2} \left[\mathrm{\mathbf{H}}_n(x) - (-1)^n \mathrm{\mathbf{H}}_{-n}(x) \right]$$ for $n=1,2,3,...$ Where $\mathrm{\mathbf{H}}_n$ are Struve functions. ...
Yuriy S's user avatar
  • 31.4k
0 votes
0 answers
36 views

Why does this sequence switch from odds to evens?

Consider a function: $f: \Bbb N \to \Bbb N$ defined as follows: $$f(n)=\bigg\lbrace\#\lbrace a_t(x) \rbrace >\#\lbrace b_t(x) \rbrace: \# \pitchfork \mathrm{id}\bigg \rbrace.$$ This notation means ...
John Zimmerman's user avatar
2 votes
1 answer
65 views

Reason behind periodic patterns in the Fibonacci polynomial sequence when expressed in terms of a natural number

A while back, a friend of mine had challenged me to decipher the pattern within the following sequence: 1, 5, 11, 19, 29, ... Staring at it for some time, the ...
HerrAlvé's user avatar
  • 187
1 vote
1 answer
135 views

Why is the sequence of sopfr($n!$) so similar to the sequence of the number of diagonals in $n$-polygons?

Could someone please enlighten me on why the sequence of sopfr(n!) (the sum of prime factors of n!) is seemingly related to the ...
HerrAlvé's user avatar
  • 187
0 votes
0 answers
50 views

Interesting pattern with continued fraction and Gamma function?

As the title says I would like to know if interesting pattern occurs starting form numerical analysis with the conitnued fraction : $$f(x)=\frac{x}{x!+\frac{2x^{2}}{x!!+\frac{3x^{3}}{x!!!+\frac{4x^{4}}...
DesmosTutu's user avatar
  • 3,025
3 votes
2 answers
155 views

Finding a formula for the sequence $\{1, 7, 17, 30, 48, 70, 95, 125, \ldots\}$

I have a sequence $$f = \{1, 7, 17, 30, 48, 70, 95, 125, \ldots\}$$ The difference between the entries of f is $$\triangledown f = \{6, 10, 13, 18, 22, 25, 30, \ldots\}$$ Finally, the difference ...
joelwilliamsemail's user avatar
0 votes
0 answers
33 views

Are there useful applications for the differences between the one-digits of (2^n) - (n^2), where n is a positive integer? 2 can be a different integer

I got curious and started listing the differences between 2^n and n^2. For example, 2^6 = 64, and 6^2 = 36, so the difference is 28. I wanted to see if any relationship could be found and I saw that ...
Drew Schuerman's user avatar
-6 votes
1 answer
82 views

Writing Mathematical function for generating a series of $30$ given numbers

I have a series of 30 given numbers as given : $0, 2, 4, 5, 6, 7, 7, 9, 8, 8, 9, 13, 9, 15, 11, 10, 10, 19, 10, 21, 11, 12, 15, 25, 11, 12, 17, 11, 13, 31$ and $12$. This was generated by the ...
Super Coder's user avatar
1 vote
2 answers
473 views

Function for a new math pattern that emerged while working on the Collatz conjecture

So, this is a follow up to my previous question on the same topic, and in this question, I used the same technique, only with a larger value. Here's the set below: S no. Resultant Value 1 227 2 ...
Tsar Asterov XVII's user avatar
2 votes
0 answers
48 views

Is it possible to find a short function for a table of points where the result of the function is always -1, 0 or 1?

For context, I am trying to solve a Code golf problem, where you need to solve a problem with a program, where the program with the shortest source code wins. There is a pretty hard problem on there ...
lxhom's user avatar
  • 121
0 votes
1 answer
52 views

Odd numbers form pairs infinitely often in this sequence?

This post discusses the integral, $$I(k)=\int_0^k\pi(x)\pi(k-x)dx.$$ I've noticed that the odd numbers seem to come in pairs separated by exactly $2$ units, but are otherwise quite randomly ...
John Zimmerman's user avatar
3 votes
3 answers
162 views

How would one go about finding the last four digits of this sum?

So I was looking through the homepage of Youtube when I found this video by Cipher. The question proposed in the video was$$\text{How do I find the last }4\text{ digits of the sum of }2+22+222+2222+\...
CrSb0001's user avatar
  • 2,424
1 vote
1 answer
101 views

Can this set of equations be extrapolated to a complete pattern?

Quick Background We have five independent variables that can each be any real number greater than zero: $d_{max}$ $v_{max}$ $a_{max}$ $j_{max}$ $s_{max}$ These variables are linked to a chain of ...
Lawton's user avatar
  • 1,675
0 votes
1 answer
64 views

What's the pattern behind the numbers on this D20 ring? [closed]

I have a D20 ring. It's a loop with the numbers 1-20 printed around it in what I initially thought was a random order. On closer inspection, I realized that they aren't random; but I'm having trouble ...
Benjamin's user avatar
  • 109
0 votes
0 answers
23 views

Distributive property of matrix multiplication help

$$a = {-\frac12(x-μ_1)^{T}Σ^{-1}(x-μ_1)}{ + (\frac12(x-μ_2)^{T}Σ^{-1}(x-μ_2))}$$ $$solution = (μ_2-μ_1)^TΣ^{−1}x-\frac12(μ_2^{T}Σ^{−1}μ_2-μ_1^{T}Σ^{−1}μ_1)$$ Simplify the following equation so that it ...
Bean's user avatar
  • 1
0 votes
2 answers
113 views

100th derivative of $ g(x) = (x^3 -4x + 7)^{30} $. Where is the pattern?

I was reviewing come Calc 1 problems, and came across one that asks us to explain what the 100th derivative of $$ g(x) = (x^3 -4x + 7)^{30} $$ would be. I computed the first three derivatives: $$ g'(x)...
RMS's user avatar
  • 348
-2 votes
1 answer
220 views

How to find a function for this set of numbers I found while working on the collatz conjecture?

So, I was looking at the Collatz conjecture, and I thought of trying to reverse engineer the patterns in a certain sense, forming branches and trees. I figured it our for Branch-1, the formula, but ...
Tsar Asterov XVII's user avatar
0 votes
0 answers
27 views

Sequence of the most significant digits of the integer tetration ${^{b}a}$: is it (eventually) periodic?

Let $F(a,b) := F({^{b}a})$ indicate the first figure (i.e., the most significant digit) of the tetration ${^{b}a} : a,b \in \mathbb{Z}^+$. As an example, we have that $a=2 \Rightarrow F(a,b)=2,4,1,6,2,...
Marco Ripà's user avatar
  • 1,069
7 votes
1 answer
175 views

Finding the maximum cycle of a given set

Problem: Given $4$ circles, we define the following set of rules: i) Any circle which contains $\ge 3 $ elements transfers exactly one of its elements to each of other $3$ circles. ii) Circles which ...
Aurora Borealis's user avatar
1 vote
1 answer
60 views

An expression for $g(x)$ where $g$ is a two-class discriminant function

I'm reading Chapter 5.2.1, The Two-Category Case of Duda and Hart's Pattern Classification, where a discriminant function for two-class classification is given by $$ g(x) = w^T x + w_0 $$ where $w$ is ...
IntegrateThis's user avatar
11 votes
1 answer
663 views

Peculiar pattern in the Collatz sequence

I created a simple visualizer to better understand the Collatz sequence beginning at each natural number. The 'redder' a color is, the quicker the starting value reaches $1$ and the "bluer" ...
Clyde Kertzer's user avatar
-2 votes
2 answers
117 views

How Are Functions Predicted? [closed]

What process or logical steps do you take to predict a function from any dataset? I don't want to predict the function using a specific dataset; I want to understand how you predict a function when ...
James Kelley's user avatar
5 votes
3 answers
198 views

What is the pattern in the powers of $\sqrt{2}-\sqrt{1}$? [duplicate]

What is the pattern in this? $$\begin{align} \left(\sqrt{2}-\sqrt{1}\right)^1 &= \sqrt{2}-\sqrt{1}\\ \left(\sqrt{2}-\sqrt{1}\right)^2 &= \sqrt{9}-\sqrt{8}\\ \left(\sqrt{2}-\sqrt{1}\right)^3 &...
Aryan Arora's user avatar
4 votes
1 answer
154 views

Is there a way to calculate the maximum length of the repeating pattern in a rational number?

I am working on a project for school in which I would need to sum up hundreds of rational values to over one trillion sig figs (done in code) however it is not practical to store each term in the ...
Hadi Beydoun's user avatar
0 votes
1 answer
63 views

Minimum number of links needed to connect every vertex of a $4$-dimensional hypercube

Let $G_2^4 :=\{0,1\} \times \{0,1\} \times \{0,1\} \times \{0,1\}$ be a set of $2^4$ points in $\mathbb{R}^4$. Which is the minimum number of straight lines connected at their endpoints (i.e., the ...
Marco Ripà's user avatar
  • 1,069
0 votes
1 answer
35 views

Last number in an upwards addition triangle, given the length of the last row.

In the lowest row the numbers 1 to n are written, then rows above consists of the sums of neighboring elements of the row below it (like in Pascal's triangle) until in the highest row only one number ...
user3284214's user avatar
0 votes
3 answers
164 views

Generalizing observations made from the sequence $1,2,4,8,16,31,57,99,...$

Generalizing observations made from the sequence $1,2,4,8,16,31,57,99,...$ The first differences between the terms are: $1,2,4,8,15,26,42...$ The second differences (the differences between the ...
user avatar
3 votes
1 answer
330 views

FFT stride pattern formula

Edit I have found a solution and I posted it below. Thanks to everyone who tried to help! Question I have implemented the radix-2 DIT FFT algorithm but I could not find a formula to determine the ...
Fra93's user avatar
  • 161
1 vote
1 answer
140 views

Finding pattern in matrix inverse

I want to see if any pattern that could be formulated exist across the rows (or equivalently , columns) of the matrix inverse (in the middle , let's name it $A^{-1}$) so that an analytical formula ...
C.C.'s user avatar
  • 850
1 vote
1 answer
110 views

Writing the recurrence $O_t=-\frac1{T_w}\sum_{i=t-T_p}^{t-1}O_i-\frac1{T_i}\sum_{i=1}^{t-T_p-1}O_i+B_t$ in terms of its initial value

I want to write the following solely in terms of its initial value $O_1$ $$ O_t = - \frac{1}{T_w} \sum_{i=t-T_p}^{t-1} O_{i} - \frac{1}{T_i} \sum_{i=1}^{t-T_p-1} O_i + B_t $$ where $T_w ...
C.C.'s user avatar
  • 850
1 vote
0 answers
48 views

Trying to find an explicit formula for the $n$th derivative of a function. [duplicate]

So my function is $$ f: \mathbb{R}\setminus \{0\}\to \mathbb{R},\; f(x)=\exp\Bigl(\frac{-1}{x^2}\Bigr). $$ My task is to find a formula for the $n$-th derivative of this function. When I wrote out ...
Emma Howe's user avatar
  • 111
1 vote
1 answer
51 views

Term for mathematical cognition concept?

I'm curious if there's a technical term for the following concept. Let's say we do a curve fit to a set of points and it conforms to the equation $y = 1.44x^2 + 82x + 5$ Obviously as a human, I'm well ...
March Hare's user avatar
7 votes
2 answers
125 views

Series expansion of $\text{Li}_3(1-x)$ at $x \sim 0$

My question is simple, but maybe hard to answer. I would like to have a series expansion for $\text{Li}_3 (1-x)$ at $x \sim 0$ in the following form: $$\text{Li}_3 (1-x) = \sum_{n=0} c_n x^n + \log x \...
Pxx's user avatar
  • 657
0 votes
0 answers
20 views

Computing the probability from a list of different events that has a sequence of different probabilities

In a problem of face recognition, I have a flow of owner's ids from the same face. This flow is generated from the application of the recognition algorithm on the stream of faces from the stream of ...
Randerson's user avatar
  • 285
0 votes
2 answers
85 views

What rule governs the sequence 3, 9, 27, 30, 33?

I recently had to complete an assessment for a job application which dealt with recognizing the patterns in number sequences and identifying what the next number in the sequence would be. One sequence ...
Juan_Vare's user avatar
0 votes
0 answers
30 views

Pattern identification in real (conically deformed) images

I'm trying to solve the following problem: I'm in an analysis process of some photographs (as taken by a camera, thus they are conically deformed). I'm already able to automatically identify some ...
José VZS's user avatar
1 vote
0 answers
57 views

Strange pattern in numbers why is the series of absolute differences always 0? [duplicate]

Put any four numbers in a row, say, 77 73 29 179. Under the first number write the difference between it and the second number. Under the second number put the difference ...
Rajat Kumar's user avatar
0 votes
0 answers
29 views

When are fractions of factorials equal to whole factorials? [duplicate]

10!/7!=6!. 6!/3!=5!. Is there something interesting happening in these examples, or are they just coincidence? Is there a way of finding other examples like these?
Brayden's user avatar

1
2 3 4 5
13