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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2
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2answers
30 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
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2answers
20 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
35 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
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0answers
44 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
34 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
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2answers
38 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
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0answers
18 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 ...
0
votes
1answer
22 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
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1answer
27 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
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3answers
18 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
24 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... ...
0
votes
0answers
32 views

Find the pattern

Can you spot the pattern? €41.04 = €58.84 €48.17 = €91.11 €59.41 = €140.04 €65.65 = €184.15 I am getting the first rate back from a web service, but when I visit their site it is suppose to be ...
0
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2answers
357 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
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0answers
13 views

k nearest neighbor density estimation

In k nearest neighbor density estimation we calculate the density using following formula For given 1D sample X={4,5,6,7,9,10,11,12,13,14) if k=3, and we do not consider on boundary samples inside ...
-1
votes
1answer
32 views

Transforming $[-3, -2, -1, 0, 1, 2, 3]$ to $[0.125, 0.25, 0.5, 1, 2, 4, 8]$

Given the range of negative/positive numbers $[-3, -2, -1, 0, 1, 2, 3]$, is there a transformation that gives me $[0.125, 0.25, 0.5, 1, 2, 4, 8]$?
19
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2answers
1k views

Understanding this pattern behind the Fibonacci sequence

To be honest, I'm pretty awful at mathematics however, when up till 6AM I do like to do random things throughout the night to keep me occupied. Tonight, I began playing with the Fibonacci sequence in ...
0
votes
2answers
37 views

Find an explicit formula for the sequence whose first few terms are 1/3, 2/3, 2, 8, 40, 240…

I am trying to find the formula for this sequence: $$1/3, 2/3, 2, 8, 40, 240...$$ I know I need to use a factorial in the formula, and then raise it to a power of something maybe? But from there I'm ...
0
votes
1answer
77 views

What makes a pattern in a sequence?

Assume a stream of characters$(c)$ where $ c \in (A, B, C ... Z)$. I need to identify patterns available in the stream. As per the definition of a pattern I should be looking for a recurring string. ...
1
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2answers
43 views

What is the pattern for this sequence?

I know that it increments by 1 until the (10n + 1)th term, where it increments by the term #. I don't know how to represent this entire pattern as an equation or summation of some sort.
0
votes
1answer
24 views

Trying to figure out a Mathematical pattern

I am given a start point, a, an end point b, and a number of values x. With that I am supposed to come up with the points between the start and end point. Below is an example ...
2
votes
1answer
27 views

Why Does This Summation Pattern Occur?

This is probably something stupid and for some reason I can't see it, but let's say you are taking the sum of the first $10^{i}$ squares. If $i=1$ we get $385$,$i=2$ we get $338350$, $i=3$ we get ...
1
vote
1answer
48 views

Find the next number [duplicate]

I am given a sequence $$1, 11, 21, 1211, 111221, 312211, 13112221, \cdots$$ what is the next number?
0
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0answers
26 views

Estimate prior for normal distributed data

I have successfully implemented a bayesian classifier using maximum likelihood. In my case I've got 2 classes and I have calculated the two $\mu$ and $\Sigma$. In my problem with a 3-dimensional ...
0
votes
1answer
50 views

how to calculate the marginal distribution of probabilistic principal component analysis

In the book Pattern recognition and machine learning from Bishop equation 12.33 states: $\mathbf{x} = \mathbf{W} \mathbf{z} + \boldsymbol\mu + \boldsymbol\epsilon$ Here $\mathbf{z}$ has a normal ...
0
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0answers
11 views

Is auto-correlation a particular and simple form of pattern in time series?

In a time serie context and considering the sign of the variation of the variable auto-correlation means that for couple of measures at (time t, time t+1) the ...
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
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0answers
13 views

Kernel Method for complex valued problems

Kernel Method are widely used in Pattern Recognition and Machine Learning. e.g Kernel PCA and Kernel Regression are used as some extension of the regular PCA and Regression. However all the kernels I ...
0
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0answers
21 views

Pattern Recognition terms a little fuzzy

I've been trying to learn more about probability and the websites I have visited are not describing the relationship to each other that well (when to use what, for what purpose in conjunction with ...
0
votes
0answers
21 views

Common or distinct covariance matrices for mahalanobis distance classifier

I'm very new to pattern recognition so apologies in advance for a newbies question. I've been experimenting with mahalanobis distance to class mean based classifiers to predict diagnoses from ...
10
votes
3answers
404 views

Consecutive Prime Gap Sum (Amateur)

List of the first fifty prime gaps: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4. My ...
1
vote
0answers
39 views

Leibniz Binary Representation of Squares

Leibniz claims to have found patterns in the square numbers and their binary representations. I cannot see any patterns at all. Here are the first ten squares and their binary representations, can ...
0
votes
1answer
30 views

Sequence and Pattern Problem of Marbles

Ellie is dropping marbles into a box one at a time in the following order: red, white, white, blue, blue, blue: red, white, white, blue, blue, blue: ... How many marbles will be in the box right ...
3
votes
1answer
89 views

Consecutive Prime Problem

Consecutive primes whose quotient of their product and sum is itself a prime number. $$ 2 \times 3 \times 5 = 30 $$ $$ 30/10 = 3 $$ $$ 3 \times 5 \times 7 = 105 $$ $$ 105/15 = 7 $$ Question: ...
2
votes
5answers
109 views

Why is $ A_1 x + … + A_n x^n $ a solution of $ \sum_0^{n} (-1)^n \frac{x^n}{n!} \frac{d^n y}{d x^n} = 0 $?

I was playing(/fiddling) around with some maths and I saw this pattern( where $ A_n $ is a constant.): $ A_1 x $ is a soultion of: $$ \frac{y}{x} - \frac{dy}{dx} = 0 $$ $ A_1 x + A_2 x^2 $ is a ...
1
vote
1answer
33 views

Bayesian Inference Problem

We have a Bayesian Network that A to D is Boolean variable. we want to calculate the probability which C and D be True and A be false. my answer sheet calculate the last result and is 0.0424. any ...
1
vote
2answers
53 views

Find if a number lies in this pattern

I have a sequence of numbers below... $1, 2, 4, 7, 11, 16 ...$ You get this list by starting at $1$ then add $1, 2, 3, 4, 5 ...$ Given a number $n$, how can I determine if it will show up in this ...
0
votes
2answers
93 views

Missing number in sequenze

A friend posted this an hour ago and it kept me busy since. Anybody has a clue what the missing number is? I understand multiple outcomes are possible but i cannot find any. There is also a ...
0
votes
1answer
52 views

Determine Patterns

I have some weather data that I would like to analyze. I have about a millions rows of data, and each row has about 100 attribute values. Each attribute value represents some measurement (i.e., ...
2
votes
2answers
203 views

Prime Number Sum Sequence (Amateur)

SOLVED: This is false Beginning with 3, add the next consecutive prime (2) and then take that sum (5) and add that to next consecutive prime (3) to get (8), and so on... $$ 3 + 2 = 5 $$ $$ 5 + 3 = 8 ...
5
votes
0answers
94 views

Find the number that follows the rules of two different series

I have this logic problem where I need to find a number that fits in 2 different series (vertical and horizontal). Each series has a rule, and once you find them, you can determine the answer. $$ ...
0
votes
3answers
109 views

Given the sequence $3, 4, 11, 16, 42\ldots $ how can I derive a general formula for it?

Given a sequence $3, 4, 11, 16, 42\ldots $ how can I derive a general formula for this sequence? Is there any optimised approach? My approach: the given series is equal to summation of $\binom{n}{k}$ ...
3
votes
1answer
107 views

Possible Prime Sum Pattern (Amateur)

Disclaimer: I’m an amateur, and have no advanced knowledge of math, so please forgive my ignorance as I’m just curious to know if I’ve stumbled upon something or not. Prime Numbers: 2, 3, 5, 7, 11, ...
0
votes
3answers
147 views

Triangular Numbers that are odd, less than 2000

The diagram below shows the $1$st, $2$nd, $3$rd and $4$th triangular numbers. (1 spot) : $1$ (3 spots) : $3$ (6 spots) : $6$ (10 spots) : $10$ The formula $n(n + 1)/2$ can be ...
1
vote
4answers
311 views

Easy as $3.14$ question

I've got the following question with the hint "Easy as $3.14$". $$2003 = 2\\1337 = 4\\7877 = 3\\5732 = 4\\8315 = 3\\4466 = 0\\0354 = 2\\8923 = 2\\8888 = 0\\0000 = 0\\4059 = 1\\2403 = \ ?$$ I need to ...
5
votes
3answers
519 views

Recognizing the sequence 1/16, 1/8, 3/16, 1/4, 5/16, …

What is the missing number? $$\frac{1}{16}, \frac{1}{8}, \frac{3}{16}, \frac{1}{4}, \frac{5}{16}, \ \ \ [?]$$ $$A. \frac{5}{4}\quad B. \frac{3}{4}\quad C. \frac{5}{8}\quad D. \frac{3}{8}$$ ...
4
votes
0answers
99 views

Adding Numbers Pattern

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
12
votes
4answers
1k views

How to solve this sequence $165,195,255,285,345,x$

This is a question appeared in a competitive exam. The question is: Find the unknown term in $165,195,255,285,345,x$ 1)375 $\ \ \ \ \ \ \ \ $ 2)420 3)435 $\ \ \ \ \ \ \ ...
1
vote
1answer
84 views

How is PI used to predict weather patterns?

I've heard that using PI to predict weather patterns is possible. I would like verification on this, and how this is possible. I can't seem to find any other sources explaining this concept. My ...
0
votes
1answer
39 views

Anyone recognize this pattern? Plotting relationship between two parameters and their response.

First time asking a question here so hopefully I can provide enough information to you guys without explaining more than necessary. I'm doing some amateurish numerical analysis in MATLAB on some ...
0
votes
2answers
64 views

closed formula for a series

The first column below is n (iterator), the second is the value, I'm trying to understand if there is a closed formula that I can use for obtaining the value given a fixed n $$n=0: a$$ $$n=1: ...