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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1answer
47 views

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

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, ...
13
votes
4answers
659 views

Eyebrow-raising pattern within 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
28 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
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' ...
2
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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
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1answer
20 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
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 ...
2
votes
1answer
58 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 ...
9
votes
2answers
126 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
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 & ...
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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
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0answers
57 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
42 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
2answers
86 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
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!
0
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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 ...
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
41 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
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 ...
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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
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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
91 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
vote
1answer
20 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
39 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 ...
-1
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 ...
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 ...
0
votes
0answers
41 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
vote
2answers
178 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 ...
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
1answer
73 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 ...
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
145 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
67 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, ...
0
votes
1answer
345 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, ...
4
votes
2answers
59 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 ...
1
vote
0answers
24 views

Can KNN theoretically be less accurate than pattern averaging?

My task is pattern recognition. I need to classify 2D matrices into an arbitrary number of classes. The question is: For pattern classification, could k nearest neighbours algorithm ever be less ...
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
28 views

proof that a density proportional to Gaussian is Gaussian

I try to develop bayesian estimation for one dimensional Gaussian with unknown $\mu$ and known $\sigma$. I got $$p(x\mid D) = \int p(x\mid\mu)p(\mu\mid D) \, d\mu =\int \frac{1}{\sigma ...
1
vote
1answer
40 views

Best algo for finding no. of steps required to convert a sequence to a palindromic sequence

[My first question of Math SE, so, HI!] I'm not sure of what the rules are around the place, but I have a straightforward question as follows... The sequences 23, 45, 23 and 23, 45, 56, 23, 23, ...
1
vote
3answers
22 views

Expression of Equation

Find the next three terms for the pattern following : (-1276),(+425),(-142),(+47) Simple pattern here.... Only pattern I can find is that, the odd number term goes up by 1134, and the even number ...
1
vote
5answers
33 views

Finding expression for pattern

This seems easy.... Pattern: 3, 6, 10, 15, 21.... How do I find expression for this? It looked easy, but I couldn't find it. I tried graphing it, but it turned out that it is not quadratic... ...