# Tagged Questions

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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### Understanding the fundamentals of pattern recognition

I'm learning now about sequences and series: patterns in short. This is part of my Calc II class. I'm finding I'm having difficulty in detecting all of the patterns that my text book is asking me to ...
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### Dimensionality effect on Fisher's Score

Consider Fisher's Linear Discriminant Analysis (LDA). Let $\mu_0 \in \mathcal{R}^D$ and $\mu_1 \in \mathcal{R}^D$ be means of the two classes. Similarly, let $\Sigma_0 \in \mathcal{R}^{D\times D}$ ...
510 views

### Stuck with handling of conditional probability in Bishop's “Pattern Recognition and Machine Learning” (1.66)

I've just started working through the book, and I'm stuck with how the author handles conditional probability in (1.66). The context is as follows. In this chapter we are working with a curve ...
327 views

### Pattern Recognition with basic probability

I am a college student and have Pattern Recognition as a course this semester and I am really struggling with it, reasons could be difference in teaching style of the instructor and different type of ...
23 views

### Self-Similar Reverse-Sum Sequences

When a number is added to its reverse (digits in reverse order), sum it. For example: 102 + 201 = 303 508 + 805 = 1313 246 + 642 = 888 Given all numbers between 0 and 10^9, discover ...
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### How to sort a list of tuples?

I am neither a mathematician, nor a computer scientist, but I have the following problem, which I cannot solve myself. I have $k$ $i$-tuples $(x_1, x_2, …, x_i)$, where $x ∈ [0,1]$. I need to order ...
51 views

### finding the missing number by pattern

In this riddle you need to find a pattern between every couple of numbers. Given numbers $5$ and $10$ there is a pattern like in the numbers $10$ and $3$. Given numbers $10$ and $15$ there is a ...
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### How can a pattern be found in a series of Numbers?

In the given series of numbers (0-9) or a similar series of numbers, How can a pattern be searched? 3 2 4 8 0 8 7 3 8 7 0 0 4 9 6 3 9 7 4 5 7 3 9 6 ...
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### Sequence patterns

Hi I'm new and I was wondering if a pattern could be derived from this. I wrote a program which printed all the numbers up until a number the user inputted, and then continuously deleted the middle ...
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### Function for numeric input output series

I am trying to find function which will give me output for corresponding inputs. ...
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### Anyone know of algorithm for compairing real planar graphs? (for OCR)

The picture pretty much explains it. I will have a collection of line segment graphs to compare against and it's okay if it's $O(n)$ here because the set is the ASCII set or smaller . I was ...
53 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 $C_{n+1}$.
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### 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 ...
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### 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 ...
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### 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 ...
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### Estimating the mean with least median of squares target

I have a set of real numbers $x_1,\ldots,x_n$. I would like estimate the mean of the set, $y$, such that the median of squares will be minimal : $\operatorname{median}(x_i-y)^2$ Is there a closed ...
554 views

### Study the number patterns and fill in the missing number

This problem seems easy but I have been working on it for quite some time with little clue. It is about finding number patterns, I have tried many different ways, which seem to work at first but fail ...
139 views

### Mapping an object's projected 3D path to a pre-defined top-down 2D path.

The title of the question may be misleading and the context simpler. Please suggest more appropriate tags for this question. Consider looking at a plane from two different perspectives. Perspective ...
226 views

### How can I count clockwise vs counterclockwise cycles in a series of (modular) integers?

I'm working with a Markov process that has a state and transition diagram like in the picture: The transition probabilities are not listed, but they are always positive, but not necessarily equal....
53 views

### Find a pattern in key => value?

Sorry if this isn't the correct place but it did seem to be! Basically, I'm coding a small test with a bouncing ball. All works well, but the problem is I need to work out the ...
127 views

### Find n term of sequence

A sequence is given: $$1,10,11,100,101,110,111,1000,\dots,a_n,\dots$$ The question is: what is the value of $a_n$ for a given $n$? I have tried a lot of patterns but was not able to meet the ...
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### 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 ...
105 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 ...
2k views

### Extract a Pattern of Iterated continued fractions from convergents

I have been working on an article at https://oeis.org/wiki/Table_of_convergents_constants where I posted a table of "convergents constants" (defined at https://oeis.org/wiki/Convergents_constant) for ...
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### Can't find the pattern [closed]

These are two sequences: I tried looking for a ratio or difference but it wasn't working $$12,20,32,\underline{\quad},22,\underline{\quad},50$$ $$6,10,16,8,\underline{\quad},22\underline{\quad}$$...
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### Sum of Odd Numbers make Squares

Look at this: 1 (+3) 4 (+5) 9 (+7) 16 (+9) 25 (+11) 36 (+13) 49 And so forth, you get the idea. Why do they make up this pattern? And is there any special name for this ...
238 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 ...
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### Finding the $n$th term for the sequence $1, \frac{1}{2}, 3, \frac{1}{4}, 5, \frac{1}{6}, \dots$

I have tried using a negative exponent. I need one statement not two, the pattern is $$1, \; \frac{1}{2}, \; 3, \; \frac{1}{4}, \; 5, \; \frac{1}{6}, \dots$$
595 views

### Probability of market movement / Trends

If you imagine a scale from -100 to 100, if the market has moved up from 0 to 40, what is the probability is will continue to 100? There is a 50-50 chance to move up or down from 0, but what is the ...
60 views

### Find the missing Item in the sequence [closed]

There is a sequence described below.What is the missing item? $5,10,?,50,122,...$
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### Finding the general term of a sequence (if there's any)

I would like to know if it's possible to find an expression for the following sequence $\;\{a_n\},\;n=0,\,1,\,2,\,3,\,\dots\;$ $1, 3 , 7, 13, 21...$ Someone would like to explain me what I have to ...
81 views

### What's the generating formula for this sequence [closed]

Can someone help me finding the generating formula for this sequence? $$[1,1,3,5,5,7,9,9,11,13,13...]$$ Thanks!
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### Sequence of $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5$

‘A sequence is formed by writing the integers the corresponding number of times as follows : 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, … What is the 800 th term in this sequence?’
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### 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. However,...
162 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, ...
408 views

### What is the 6th term of the sequence? [closed]

Sequence: ABC; 1A1B1C; 111A111B111C; 311A311B311C; ... What is the 6th term of the sequence? ...
64 views

### Need help modifying this binomial expansion

The binomial theorem states that $$(A+B)^n=\sum_{k=1}^{n}{n \choose k}A^{n-k}B^k$$ I need help expressing the following summation as a modified binomial expression: \sum_{k=1}^{n}n!{n-1\choose k}...
I'm trying to figure out the rule that's producing the series below. The first column is the factorials $1!,2!,3!,4!,5!,6!$ But I can't figure out what else is going on. So I know the next row will ...