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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104 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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3answers
117 views

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 $$1, \; \frac{1}{2}, \; 3, \; \frac{1}{4}, \; 5, \; \frac{1}{6}, \dots$$
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431 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 ...
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3answers
138 views

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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68 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. ...
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1answer
97 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, ...
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1answer
263 views

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

Sequence: ABC; 1A1B1C; 111A111B111C; 311A311B311C; ... What is the 6th term of the sequence? ...
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2answers
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 ...
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1answer
161 views

Trying to figure out the pattern in this series

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 ...
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1answer
36 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 ...
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1answer
784 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, ...
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298 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 ...
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2answers
74 views

Evaluate an unknown operator

I have a simple question but I can't seem to be able to solve it. Given that: 25 ╧ 17 = 267 35 ╧ 23 = 373 45 ╧ 15 = 465 what is ...
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2answers
42 views

What is the general stragety for conjecturing a formula based off a pattern?

Is it simply to guess and evolve a answer until it gets closer or is there an approach? Ex: Find the formula for: $a_k = \frac{a_{k-1}}{2} + 1$ where $a_0 = 1$. One would go: $a_1 = 3/2, a_2 = ...
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4answers
165 views

How to represent the $n$th number in the sequence $1,3,5,7,1,3,5,7,\dots$ as a closed form?

I'm given the repeating sequence $1,3,5,7,1,3,5,7,\dots.$ I must determine a formula for the $n$th term of the sequence. I have tried the triangle method, but since this is a repeating series it is ...
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3answers
111 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 $\binom{n}{k}$ ...
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1answer
117 views

Creating coexistent patterns, with several pattern-less systems

I'm a young musician, as well as a computer programmer. My understanding of math is formed well to my needs, but I am by no means a mathematician, but the field is very interesting to me. I have come ...
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1answer
429 views

Find the next number in this sequence

I have a homework. It seems to be an easy sequence but I can't get the answer. So, What is the next element? $$2, 7, 10, 13, 23, 34,?$$ What would be the solution out of these numbers? 45 or 49 or 58 ...
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2answers
112 views

Finding pattern (2,7,8,3,5)

What would replace $Z$ in the following sequencing? $$\begin{matrix} 2 & 3 & 4 \\ 7 & 6 & 5 \\ 8 & 7 & 1 \\ 3 & 0 & Z \\ 5 & ...
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1answer
97 views

A lemma regarding cones covering $\mathbb{R}^d$

Added: Pointers to some references with the same conclusion as the wolloing lemma may be helpful to understand it, and are appreciated. In A Probabilistic Theory of Pattern Recognition By Luc ...
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1answer
82 views

Game statistics: Extracting interesting patterns out of users and level

I made a small game and in course of time collected fair amount of data between users and level The level chart is long (120 levels) but looks somewhat like this $$ \begin{array}{|c|c|} ...
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1answer
55 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 ...
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5answers
67 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 ...
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1answer
57 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., ...
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2answers
408 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: ...
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1answer
42 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 ...
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2answers
69 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: ...
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2answers
36 views

Equation for value of p given x

I have a set of numbers: $\begin{array}{r(22)}x \in \{ 1,& 2,& 3,& 4,& 5,& 6,& 7,& 8,& 9,& 10,& 11,& 12,& 13,& 14,& 15,& 16,& 17,& ...
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1answer
57 views

How can I figure out the total solutions in this Combinatorics problem?

Imagine you have a sequence of cards, each having a unique set of features. Example features : letter (A, B, C), number (1, 2, 3), and color (Red, Green, Blue) Some example cards : A1Red, B1Blue, ...
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1answer
26k 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.. ...
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1answer
156 views

Find the pattern, what is the correct number in that spot, explain the answer

we are given the following matrix: $\begin{pmatrix} 9 & 38 & 47 &4 \\ 6 & 35 & 42 & ? \\ 12 & 21 & 23 & 27\end{pmatrix}$ The number that goes in $?$ is $-5$. I ...
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1answer
102 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. ...
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1answer
203 views

Expression for Sum of Multivariate Gaussian Random Vectors

Consider two multidimensional random vectors $x$ and $z$ having Gaussian distributions $P(x)=N(x\mid\mu_x,\Sigma_x)$ and $P(z)=N(z\mid\mu_z,\Sigma_z)$, respectively, together with their sum $y=x+z$. ...
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1answer
154 views

What is the pattern here? Q-function - SOLVED

I've got the following problem: The difinition of the funtion: Q(S,M). The purpose is to find the max number of possibilities how to write the funcition. ...
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1answer
66 views

Identifying a pattern in an array

Is there a way to identifying a pattern and/or recursive function for an array? If yes, how can I do this. Could anyone please help me with some information and/or resource for this? Any help is ...
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1answer
180 views

Finding the mean (or pattern) of a set of related values in a matrix discarding those that are too different.

this is my first question here so I am not sure if it is a valid one. I am currently facing a mathematical problem that is not so hard to solve, but given the accuracy i need in the results I would ...
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1answer
493 views

Equations and Pattern formulas problem solving

I have this question to answer and I need help with finding or creating a equation. You own a license plate manufacturing company. Write a formula or equation that takes a population and ...
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1answer
48 views

Finding patterns in seemingly arbitrary pairs of numbers

I don't work (directly) in mathematics (I'm a programmer), but I see numbers every day. Today I came across an issue where some totals were off, and was sent a list of the last 9 examples of the ...
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2answers
111 views

Can't figure it out, why is this answer is right. By what pattern

I found this example in some old book and can't figure it out, why is this answer is right. Would like to get an explanation to it. Thanks in advance. I don't have reputation over 10, so I uploaded ...
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0answers
20 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, ...
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0answers
62 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, ...
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0answers
21 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 ...
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0answers
38 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 ...
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0answers
20 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' ...
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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 ...
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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
41 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 ...
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1answer
54 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.
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0answers
52 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 ...
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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!