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
56 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 ...
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0answers
446 views

Finding an unknown number in the middle of a number sequence

I've stumbled across a very peculiar number sequence and it was bugging me for a while now, i would really like to find out a way to dissect and work out the number that is missing, here's the ...
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1answer
103 views

Finding an expression to represent this pattern

Is there a method to find a math expression for a given pattern? I have this pattern and I am very curious to find out how can I generate it. ...
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0answers
37 views

Trace of a product of a recursive series of non-full rank matrices

Let $H$ be a $m\times n$ matrix that is not full rank. Hence $H^T H \neq \mathbb{1}_{m\times m}$. Can we say anything about the diagonal entries, or the trace, of matrix products of the form: $P_0 = ...
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2answers
125 views

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 ...
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0answers
498 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 ...
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0answers
130 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 ...
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1answer
76 views

Is there a shorter way to write an equation with a clear pattern?

I have this simple expression: $$\left(\begin{array}{l} 1\\ +(A)\\ +(A+B)\\ +(A+B+C)\\ +(A+B+C+D)\\ +(A+B+C+D+E)\\ +(A+B+C+D+E+F)\\ +(A+B+C+D+E+F+G)\\ +(A+B+C+D+E+F+G+H)\\ +(A+B+C+D+E+F+G+H) ...
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1answer
207 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 ...
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0answers
51 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 ...
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0answers
207 views

Theoretical proof of convergence of sequential weight update procedure (Neural Networks and Machine Learning)

My question is at the bottom. (Most of the descriptive words come from Chris. Bishop's Neural Networks for Pattern Recognition) let $w$ be the weight vector of the neural network and $E$ the error ...
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2answers
118 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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2answers
87 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 ...
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2answers
102 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 ...
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3answers
1k 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) ...
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3answers
32 views

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 ...
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2answers
159 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
118 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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2answers
512 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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2answers
52 views

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 ...
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3answers
80 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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3answers
314 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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3answers
113 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
131 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
339 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
165 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
43 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
2k 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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4answers
169 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
3k views

What is the next picture in this sequence?

I was reading a book on logical reasoning and came across the following: Can anyone give me the answer to the question. We want the next sequence ?
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2answers
59 views

Find the number to replace the question mark in between two pairs of numbers

Here is the problem: I have to find the number to replace the question mark. I know there is a series or a pattern to find it any hint will be very helpful.
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2answers
182 views

Find a formula for the sequence 1,3,6,10,15,…

Write a formula/formulae for the following sequence: b). 1,3,6,10,15,... I am not getting any pattern here, from which to derive a formula. This sequence does not look like the examples I ...
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3answers
73 views

Is there a way to write $\dots 2(2(2(2+1)-1)+1)-1 \dots$ in closed form?

It's something like a sequence I'm working with and a part of it has coefficients, which go $3$, $5$, $11$, $21$ and so on. I was wondering if it's possible to find a (closed) formula dependent on say ...
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3answers
411 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
85 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
45 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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2answers
47 views

Is there a general expression for this pattern?

I am trying to find a general expression for this pattern, I know it must be something stupidly easy but I can't seem to find it. Could somebody please help me?
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1answer
69 views

State machine scenario: finding invariant

Alice, Bob, and Charles want to evenly distribute a dozen doughnuts. Initially, Alice has 5, Bob has 3, and Charles has 4. However, they want to do it according to the following rules: 1) Bob may ...
0
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3answers
113 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 $\binom{n}{k}$ ...
0
votes
1answer
134 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
966 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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1answer
105 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
84 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|} ...
0
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1answer
25 views

Determining the pattern in a basic numerical series

In the context of finding the series solution for a variable coefficient ODE, I have to determine if a consistent pattern exists between the following numbers: $\frac{-1} {3!},\frac{-1} ...
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1answer
22 views

how to find formula that matches pattern

I have a pattern that I'm struggling to find the formula for. For inputs of 0 - 3, the expected result is 0. For inputs 4 - 6, the expected result is 3. 7 - 9 should output 6. 10 - 12 should output ...
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1answer
22 views

Help figuring out a simple formula?

I have an alpha value with a range of 0.0 - 1.0 as well as a value N. If the alpha value is 0.5, I want to make no change to N. If the alpha value is 0, I want to double N. If the alpha value is 1.0 I ...
0
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1answer
28 views

What is a permutation pattern?

The wikipedia entry for permutation pattern gives this as an example: For example, in the permutation π = 391867452, π1=3 and π9=2. A permutation π is said to contain the permutation σ if there ...
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1answer
113 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
71 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 ...