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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17 views

Struggling to understand multi-class logistic regression

It is well defined that given a data set of $N$ $i.i.d$ observations $\mathbf{X} = \{\vec{\mathbf{x}}_1, \dots, \vec{\mathbf{x}}_n\}$, along with corresponding target values $\vec{\mathbf{t}} = {t_1, ...
0
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3answers
48 views

How do I solve the missing number in a series using the application of calculus?

5,6,10,19,35, ... I know the way to solve this with the basic way i.e. finding the difference. Otherwise, look for the square and difference since the number is growing kind of exponentially. ...
1
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2answers
35 views

Is there a obvious pattern between a Catalan number and another?

I know that $ C_n = C_0 C_{n-1} + C_1 C_{n-2} + C_2 C_{n-3} + \cdots + C_{n-1} C_0 $., but I was wondering if there was a more obvious pattern between $C_n$ and $C_{n+1}$.
-3
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1answer
38 views

What is the member in the last set of this pattern? [closed]

(42,15,3) (24,20,2) (?,12,4) ? indicates the number I do not know
2
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1answer
31 views

Derive a formula for the number of small square base pyramids required to create a bigger pyramid?

To quote from the problem statement: "Pyramids are built using smallest pyramids of "level 1", that are used as building blocks for higher levels. Stacking pyramids of "level 1" to create ...
0
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0answers
61 views

Is there a pattern that can be seen in this sequence?

I can't seem to find any pattern, perhaps a fresh view from one of you guys can point me to the right direction: 14898997873, 16483634594, 17241926510, 16427260053, 19933377255, 7467660818, ...
11
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3answers
199 views

Digital root of twin prime semiprimes

It appears that the product of any pair of twin primes (excluding the first pair 3 and 5) yields a semi prime whose digital root is equal to $8$. Example: $$ 17 \cdot 19 = 323 $$ The digital root of ...
0
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0answers
15 views

Pattern recognition and machine learning - Bishop: Difficulty deriving (2.111) and (2.112)

I'm having a hard time deriving (2.111) and (2.112) in this book (it's on page 110/703). Here is what it says: Finally, we seek an expression for the conditionalp(x|y). Recall that the results for ...
0
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0answers
35 views

Solving a Recurrence for a Mathematical Game

The problem is: Two players take turns removing coins from a pile. There are initially $n$ coins, and on each turn, a player can remove $a_1, a_2, \dotsc, a_k$ coins. The player who cannot remove ...
1
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1answer
39 views

Listing elements from set-builder notation, and vice versa

I have trouble translating from a set-builder notation to a "dotted set" $$\{\ldots,v_1,v_2,v_3,\ldots\}$$ and vice-versa. Set-builder to dotted set: $$\begin{align*} A &= \{5a+ 2b : a,b \in ...
1
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1answer
101 views

Is there a pattern of the length between one even Fibonacci number and another?

I had seen a math problem asking for the sum of all even Fibonacci numbers up to 4 million, but I still need to know this: Is there an obvious pattern of the distance between a even Fibonacci number ...
5
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0answers
67 views

What Constitutes a Pattern

Mathematics is often referred to as the "study of patterns." What I'm wondering is whether there is somehow a technical way to describe a pattern. For the length of this question let's assume that ...
1
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2answers
39 views

Extracting formula from a pattern(table)

I am trying to solve a problem that requires me to extract a formula from a table, and the table has the following pattern, \begin{array}{c|c|c|c|c|c|c} \text{row 6} & \text{26}& ...
0
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1answer
91 views

Brain-explosion pattern of primes and the number 30? [closed]

Prime numbers. Elusive little snips. They give you a warm trail with a dead end. Here's another one of those pattern 'trails': $$30$$ Normal number? How about 'expanding' outward? $$29, 30, 31$$ Yea, ...
45
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4answers
4k views

Eyebrow-raising pattern of number of primes between terms of the Fibonacci number sequence?

So, $$1,1,2,3,5,8,13,21...$$ Any connection to primes?...it appears not. However, in between the Fibonacci numbers are how much primes? Let's see: 1 and 1 ZERO 1 and 2 NADA 2 and 3 ZILCH 3 and 5 ZIP ...
1
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0answers
34 views

Calculating a formula for variables with multiple values equaling the same total

I'm having a bit of trouble puzzling a formula for some code I'm using to develop a piece of software. I'm not very savvy with what the technical terms for all of what I'm describing are, but I'll try ...
0
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0answers
17 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' ...
2
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0answers
35 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
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1answer
44 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 ...
0
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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
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5answers
65 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 ...
2
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1answer
61 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 ...
8
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2answers
138 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 ...
0
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1answer
27 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 & ...
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2answers
39 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
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1answer
53 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
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0answers
63 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 ...
0
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0answers
50 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
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2answers
95 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
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0answers
9 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!
0
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1answer
31 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 ...
6
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2answers
297 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
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0answers
12 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
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0answers
65 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: ...
2
votes
1answer
35 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
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3answers
106 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
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2answers
42 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 ...
1
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2answers
48 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
85 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
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1answer
100 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
128 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 ...
1
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1answer
30 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 ...
2
votes
1answer
40 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
100 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 ...
-1
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2answers
66 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
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1answer
49 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
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0answers
53 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 ...
37
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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 ...
0
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0answers
64 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 ...
1
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2answers
250 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 ...