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, ...

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-3
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5answers
430 views

How to solve the sequence: $87, 89, 95, 107, ?, 157$

This question appeared in a competitive exam. The question is: Q. Find the unknown term in $87,89,95,107,?,157$ 1)127 $\ \ \ \ \ \ \ \ $ 2)122 3)139 $\ \ \ \ \ \ \ \ $ ...
0
votes
0answers
9 views

Frequency of a specific date, time, DoB combination/'palindrome'

Apologies if this isn't the correct forum to ask - I'm a regular Stack code user, this had me scratching my head for a while and just curious if someone a lot smarter than me can tell me how 'unique' ...
0
votes
1answer
19 views

Generate random number based on a certain pattern and able to test against the pattern

I have very little idea about random numbers and patterns, so I am not sure whether this is actually possible or not. I want to generate random numbers, that will follow a fixed pattern (perhaps this ...
2
votes
0answers
32 views

Trade-off among symmetries

Take a set $X \in \mathbb{R}^2$ of nonzero measure $\mu(X) \neq 0$. I am attempting to design a set that has the following symmetries (continuous or discrete) $1.$ Scale symmetry $2.$ Rotation ...
0
votes
0answers
15 views

Need help on Pattern problem

Hi I have problem on Pattern problem as shown picture. I can find only A B C butpending on D. Thanks. E.g. (First table) A = 7-1 =6 B = 7-6 =1 C = 7 + A = 7 + 6 ...
0
votes
5answers
60 views

How can I find the general formula for the following real sequence

How can I find the general formula for the following real sequence $$(x_n)_{n \ge0}=(1,0,-1,0,\frac{1}{2},0,\frac{-1}{6},0,\frac{1}{24},0,\frac{-1}{120},\ldots)$$ I just know $x_0$ to $x_{10}$ so how ...
9
votes
2answers
125 views

Finding pattern

Just a puzzle. \begin{matrix} 2 & 9 & ? \\ 11 & 33 & 66 \\ 8 & 3 & 27 \\ \end{matrix} The options are $35$, $40$, $45$, $55$. $45$ is false. I ...
2
votes
1answer
49 views

How to show that $p(t|x,\mathbf x,\mathbf t)= \int p(t|x,\mathbf w)p(\mathbf w|\mathbf x, \mathbf t)d\mathbf w $

The following paragraph is approximately cited from Bishop's book, Pattern Recognition and Machine Learning. In curve fitting problem, we have training data $\mathbf x$ and $\mathbf t$, along ...
1
vote
1answer
69 views

T-shaped polygons

Is there any coefficient that can indicate T-shaped polygons ? Examples of T-shaped polygons:
3
votes
3answers
8k views

Finding formula for the nth partial sum

A few days ago, I asked for some clarification about pattern recognition and the n-th partial sum for infinite series. Although the explanation given was top-notch (thanks again), I'm still having ...
1
vote
2answers
811 views

How to find the pattern?

I'm challenging myself to figure out the mathematical expression of the number of possible combinations for certain parameters, and frankly I have no idea how. The rules are these: Take numbers ...
0
votes
1answer
25 views

What does this quantity measure?

Consider this list of numbers: $$\begin{bmatrix} 59 \\ 148 & 0.60 \\ 200 & 0.26 & 1 \\ 250 & 0.20 & 1.25 \\ 290 & 0.14 & 1.45 \\ 325 & 0.11 & 1.625 \\ 360 & ...
0
votes
2answers
33 views

Generate equation from pattern

What equation describes the growth pattern of this sequence: P = 5,25,35,55,65,85,95... Heres the diferences: 5 (20) 25 (10) 35 (20) 55 (10) 65 ... I have tried the P = Ax + B but it doesn work ...
0
votes
1answer
48 views

Pattern Finding in terms of previous terms

Find the next terms of the pattern: $$ 1,4,24,192,2120,31140,566202 \dots$$ Tell the pattern expression. I have already tried Lagrange interpolation. But it is not accurate enough.
1
vote
0answers
56 views

Elusive closed form for card permutation problem

Does a closed form formula f(n) exist for the two rightmost columns? The two question marks are meant to be 0. The diagram is a summary of the numerical results from original question: Permutations ...
28
votes
7answers
2k views

Are Mersenne prime exponents always odd?

I have been researching Mersenne primes so I can write a program that finds them. A Mersenne prime looks like $2^n-1$. When calculating them, I have noticed that the $n$ value always appears to be ...
0
votes
2answers
84 views

How to find a formula for a non-obvious sequence of numbers?

Suppose I have an "arbitrary" sequence of numbers and as a convenience, I want some type of concise formula to be able to generate/regenerate that exact sequence. How can I do it? Can this be done ...
0
votes
0answers
40 views

Why does this matematical pattern occurs here?

The actual question goes like this A room has N (1 to N inclusive) bulbs and N switches. N people go in one by one. 1st person goes in and toggles none of the switches. 2nd person goes in and ...
0
votes
1answer
23 views

Pattern finding of last few digit of a^b

The question is:Find the last two digits of 9^2013.(No calculators allowed to solve this question.) Options: (A)01 (B)29 (C)41 (D)81 (E)89 From this point,I will show my working, 9^2=81(Last Digit ...
0
votes
0answers
8 views

Discriminant Functions of two classes sharing same covariance matrix

How can i find the discriminant functions of two classes having same diagonal covariance matrix with different means? (their feature vector is two dimensional) Thank you!
6
votes
2answers
281 views

Permutations to satisfy a challenging restriction

In a stack of n distinct cards in order {1,2,3,4,...,n} from top, define distance between 2 cards as the number of cards between them. 2 cards are neighbours if they're adjacent in original ...
0
votes
0answers
9 views

Recognition rate prediction as a function of number of distractors

What would be a formula for extrapolating behavior of an algorithm that was tested with small number of false positives, say $10$ or $100$ but I want to know the rate with $1000$. E.g., the ...
1
vote
0answers
37 views

Why use two slack variables in the support vector regression formulation?

I am learning support vector regression but cannot fully understand the rational of the slack variable tricks in its formulation. The original optimization problem for SVR is as follows: ...
0
votes
1answer
25k views

I don't see the pattern.. does anyone understand this..? [duplicate]

Note.. the numbers are actually in a 7 x 6 grid.. graphics did not show here.. ...
2
votes
1answer
34 views

how to calculate nth term of mth row of this table?

there is a table which grows as 1,1 1,1,2 1,1,3,3 1,1,4,4,6 1,1,5,5,10,10 1,1,6,6,15,15,20 .....and so on If i want to find an specific element of the table ...
4
votes
3answers
105 views

Rewriting exponents as sigmas, is this a thing?

Is this a thing? If not, can anyone help me out on this? So I saw this a while back.$$\sum_{i=0}^n(2n + 1) = n^2$$ For positve n. This is interesting, and I wondered if I could write any n^x in ...
1
vote
2answers
40 views

Divide By Vector

In linear Naive Bayesian with multivariate Gaussian distribution: $$\mu_i , \mu_j, x$$ are all vectors of the same dimensions. So I have this equation that does a vector division by somehow and I ...
0
votes
2answers
42 views

This question is for sequences, how would I go about solving this?

Find a general term (expressed as a function of the variable $n$) for the following sequence: $$\{a_1, a_2, a_3, a_4,\dots\}=\left\{\frac{4}{8}, \frac{16}{64}, \frac{64}{512}, ...
2
votes
1answer
78 views

Why 312 Avoiding?

I have recently had the chance to attend a nice talk in Combinatorics, and once the speaker alluded to the famous 312-avoiding pattern problem, I was reminded of the following question I have had ...
1
vote
1answer
99 views

Are there multiple ways to complete a sequence?

Given sequence F as described: $$F=\{\frac{0}{2}, \frac{2}{3}, \frac{4}{5}, \frac{6}{w}, \frac{8}{11}, \frac{10}{13}, \ldots\}$$ The value of $w$ would be $7$ because all divisors are prime numbers. ...
2
votes
4answers
89 views

Pattern Recognition - How to solve this problem? [closed]

A general term of the sequence $$ -8,-7,-10,-1,-28,53,\ldots $$ can be expressed as $\dfrac{a-b^{n-1}}{4}$, where $a$ and $b$ are integers. What is the value of $ab$? Teach me how to solve this ...
3
votes
3answers
272 views

Largest number on multiplying with itself gives the same number as last digits of the product

What is the largest number on multiplying with itself gives the same number as last digits of the product? i.e., $(376 \times 376) = 141376$ i.e., $(25\times 25) = 625$ If the largest number cant ...
1
vote
1answer
19 views

Set of Numbers when added in any combination always produce unique result

What I'm looking for is a set of numbers that when added in any combination they always have a unique sum? Is this called something? I have searched on google for hours and I'm having a hard time ...
0
votes
0answers
38 views

In kernel rules, why is a regular kernel necessarily bounded?

Request from a dabbler in measure theory. Here a kernel merely designates a real-valued function. Quoted from "A Probabilistic Theory of Pattern Recognition", Luc Devroye, Laszlo Gyorfi, Gabor ...
2
votes
1answer
38 views

Finding the best fit of 3 categories ( restaurants/meal/person analogy problem )

I have this problem that sounds tedious and long and I'm not sure if there exist an intuitive way to solve it. The problem is related to image recognition but I will try to give an analogy to it You ...
2
votes
2answers
87 views

What is the next row of this pattern?

I'm attempting to help my little sister with her Algebra 1 homework, and this problem showed up. I can't for the life of me figure out the pattern; I was hoping someone would be able to. Here's the ...
36
votes
5answers
6k views

If a prime number is reversed, and then appended to itself, why is the result always a composite number?

$2 \Rightarrow 22$ which is a composite number. $37 \Rightarrow 3773$ which is a composite number. $523 \Rightarrow 523325$ which is a composite number. $8123 \Rightarrow 81233218$ which is a ...
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votes
2answers
57 views

I found a strange number pattern in Base 10. Does anyone know what it means?

I was trying to think of a good equation for texture smoothing to be used in programming. I came up with this. With texture smoothing however it must be based on division. $01$ to $10$ = $9$ or $3^2$ ...
0
votes
1answer
42 views

Hypersphere - Pattern matching using Centroid, Radius and Diameter

I have a hyper-sphere formed with set of $n$-dimensional data points. I could calculate centroid ($X_0$), radius($R$) and diameter($D$). Using these $X_0, R, D$, how I can find whether the a given ...
2
votes
0answers
49 views

Question regarding pattern recognition in a table

Knowing this is a seemingly weird question, I do believe I should provide some additional context . One of our university professor's has a terribly peculiar habit . Namely, each year, the students ...
2
votes
1answer
71 views

Is there a pattern for this sequence? [closed]

I've been looking at this and I thought there might be a pattern but I can't seem to find it. There are always $4$ elements, and they can be divided into $1, 2, 3, 4$ subsets ("chunks"). For example ...
1
vote
2answers
165 views

How to use a difference table to find a formula for a given sequence?

Given a sequence, how do you get a "rule" from its difference table? For example; 1, 2, 3, 4, 5, 6 1, 1, 1, 1, 1 Or 1, 2, 7, 16, 29 1, 5, 9, 14 4, 4, 4 I haven't really explored this ...
0
votes
2answers
384 views

Logic of numerical series

One of our colleagues has written a numerical series to the whiteboard in our breakroom. Nobody until now could solve the logic behind this series: ...
1
vote
1answer
38 views

In what way are the elements in this list of numbers most simply related?

I will try to keep this as math related as possible, though I intend to use this from a computer science standpoint. Hopefully you can forgive some of my annotations. Consider an ordered list of ...
2
votes
2answers
34 views

Find solution to pattern

Ok so I have this pattern [1]0-50 [2]51-150 [3]151-300 [4]301-500 [5]501-750 [6]751-1050 [7]1051-1400 etc forever What I need is to be able to take in the second ...
1
vote
1answer
140 views

Blocks of Pyramid Pattern Expression [duplicate]

There is a pattern following, and trying to find the algebraic expression Each layer (from the top). Diagram. So the first layer has 1, second has 4, third has 9, and the fourth has 16. That's ...
3
votes
3answers
66 views

Is there any pattern to pythagorean triples where there are two a-b pairs for one c?

I've found lots of Pythagorean triples like this, where there are two triples with the same c. Is there any pattern to them $17^2 + 144^2 = 145^2$ $24^2 + 143^2 = 145^2$ examples: (by c) 145, 185, ...
1
vote
0answers
52 views

Other Patterns in Triples

I have the following 20 triples generated by polynomial distribution: $$\begin{matrix} (2,4,5)&(2,3,4)&(2,3,5)&(1,4,5)&(2,2,4)\\ ...
0
votes
1answer
321 views

Number pattern prediction algorithm [duplicate]

Since childhood we are all familiar with the task of predicting the next number in a sequence. From something simple like, $2,4,6,...$ and $4,9,25,...$ to something more complex like, ...
3
votes
2answers
55 views

How to solve linear, second order ODE with Frobenius method with a difficult recurrence relation?

The ODE in question is: $$4xy''+2y'+y=0$$ Shifting the power series of each term so that they are all raised to the power $(n+r)$ will yield this recurrence relation: $$a_{n+1}={a_n\over ...