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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2answers
30 views

How to count the number of x in a rows in a larger set.

For example, I have 4 in a row like so: xxxx I can see that it has 2 xxx in it and 3 xx. ...
0
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0answers
13 views

all possible patterns [closed]

I have 13 football games and each has only 3 posaibilities thats is home-win or draw or away-win (1-X-2). I want to find all possible patterns of winning all the thirteen games eg (22XX11X2111X2). HOW ...
0
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1answer
27 views

Recognising patterns and turning it into a formula

On a coordinate plane lets name a move dot A. The dot A moves each day. On day 1, it moves 1 in the x- axis direction. On day 2 it moves $2^2$ in the y- axis direction. On day 3 it moves -$3^2$ in the ...
3
votes
1answer
45 views

Analysis of coefficients of $x^k+\dfrac1{x^k}$ polynomials

Given $x+\dfrac1x=n$, I derived several expressions in terms of $n$ to solve for $x^k+\dfrac1{x^k}$ and put them in a chart as shown below. My questions is how are the coefficients of these ...
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0answers
8 views

Computing Positive definite covariance matrix in Variational Bayes GMM

This question is about a part of variational Bayes problem for GMM. (more in Bishop, Pattern recognition and Machine learning, part $10.2.1$). We are looking for $q(\mu_k,\Lambda_k)$, so we have: $$ ...
0
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1answer
47 views

How to select an item from a set with constraints, and finding when the pattern repeats.

I am trying to solve the following problem with constraints that are explained below. Assume there are customers walking into a restaurant and you want to assign them to different waiters. With the ...
0
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1answer
28 views

Binomial Coefficient Explanaition

Let $n\in\mathbb{N}$ and let $k\in\{0,\ldots,n\}$. Explain why it follows from $$\binom nk=\frac{n}{1}\times\frac{n-1}{2}\times\frac{n-2}{3}\times\cdots\times\frac{n-k+1}{k}$$ that $$\binom ...
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1answer
19 views

Binomial Coefficient Pattern [closed]

Let $n$ $\epsilon$ N and let $k$ $\epsilon$ {0,...,n}. Explain why it follows from ${n \choose k}$ = ${n \choose k-1}$$\frac{n-k+1}{k}$ that ${n \choose k}$ = ...
3
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2answers
51 views

I think I've found all roots to $f_k(x)=\sum_{j=1}^k x^j-x^{-j}$ for any $k$ - how to prove it?

Conjecture: The set of unique roots of $$f_k(x)=\sum_{j=1}^k x^j-x^{-j} \;,\;\; x \not=0$$ is given by $e^{i \pi \phi_k}$, where $$\frac{1}{2}\phi_k=\{0, \frac{1}{2}, ...
2
votes
1answer
26 views

$k-1$st derivative of a degree $k$ polynomial

I know this is going to come across as a very strange question, but it's important that I know the answer. Say I have a degree $k$ polynomial (for my case, I need it to be a complex-valued polynomial ...
2
votes
5answers
330 views

What number comes next in the sequence $7, 16, 8, 27, 9,…$? [closed]

What number comes next in this series? $$7, 16, 8, 27, 9,...$$ I thought it was $38$, but I'm wrong. It is a multiple choice, and options are $27, 10, 40, 37$. Don't worry - I'm not cheating on ...
-1
votes
2answers
78 views

Cant find the pattern [closed]

These are two sequences: I tried looking for a ratio or difference but it wasnt working $$ 12,20,32,\underline{\quad},22,\underline{\quad},50 $$ $$ 6,10,16,8,\underline{\quad},22\underline{\quad} $$ ...
0
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0answers
19 views

Lower bound of Nearest Neighbour Rule

It is stated often as a matter of fact that the lower bound for Nearest Neighbour rule is the Baye's rate. However when I tried to mathematically prove it,I hit a dead end. For reference : Error for ...
1
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0answers
75 views

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 ...
0
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2answers
50 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?
0
votes
1answer
32 views

Quadratic number pattern equation

May I know how do I form a quadratic number pattern equation? I cant seem to form one on my own. 1500, 1519,1536, 1551,1564.
1
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1answer
44 views

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 ...
0
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0answers
23 views

Where do I need to use regularization parameter lambda for better results?

In polynomial curve fitting problem as below, if $y(x,w)$ is the output when $x$ is the input vector, $w$ are the coefficients and and $M$ is the order of polynomial.. And if $t_n$ is the target ...
10
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1answer
102 views

Relationship between primes and practical numbers

This is my first post here. I am a musician, and not a mathematician, but I enjoy doing things to prime numbers and seeing what comes out. I have defined a sequence which takes the following values ...
-9
votes
3answers
176 views

Interesting patterns to the algebraic solutions of polynomials [closed]

In yet another attempt to find the solution to the quintic polynomial, I started looking backwards at the solutions to the quartic, cubic, quadratic, and linear polynomials to see if I could pick up ...
1
vote
1answer
65 views

Did the U.S. Army use a formula to evaluate fitness performance?

While writing a web app to calculate one's score on the Army Physical Fitness Test (APFT), I grew tired of simply retyping this chart: ...
0
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2answers
102 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.
2
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3answers
67 views

Is there a way of making “guess the next number in the sequence” rigorous?

This is maybe more of a question for matheducators.SE than math.SE but I'm more interested in the math than the education. A common problem given to middle and high school kids (at least in America) ...
5
votes
1answer
167 views

Please, help to identify this numerical constant

I'm trying to find an answer to this question. Let $K(k)$ be the elliptic integral of the first kind and $K'=K(\sqrt{1-k^2})$. According to Abel's theorem (see this link) we know that if ...
1
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3answers
61 views

Is there a pattern to the golden ratio number figures?

The golden ratio or phi is 1.6180339887498948482045... I am wondering if there is a pattern in the numbers so given a certain set of figures, you are able to figure out the rest of the figures ...
3
votes
1answer
54 views

Fibonacci-Like Sequence: Breeding Rabbits

I came across the following question on a math test: Suppose Fibonacci's research in the breeding habits of rabbits has been adjusted. They are now believed to be fertile after $2$ months of life, ...
5
votes
2answers
413 views

Has anyone seen this pattern that evaluates to $-\frac{1}{3}$ always?

I was recently doodling and came upon an interesting pattern. Beginning with $0$, add $1$, subtract $2$, divide by $3$, and multiply by $4$. Then add $5$, subtract $6$, divide by $7$, and multiply by ...
0
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2answers
47 views
-2
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1answer
55 views

How to find the 999th shape in a pattern?

The pattern is of a triangle followed by 3 stars and 4 circles and it continues to repeat. What will the 999th shape in the pattern be? Explain how you can tell.
1
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1answer
39 views

Function for numeric input output series

I am trying to find function which will give me output for corresponding inputs. ...
0
votes
1answer
26 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} ...
0
votes
2answers
334 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 ...
0
votes
2answers
58 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 ...
0
votes
1answer
71 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 ...
-2
votes
2answers
61 views

Find mising numbers from a sequence 1,4,?,16,?,36,? [closed]

Please help me find the number absent in the line for the follow sequence $1,4,?,16,?,36,?$. For example I know the absent number in the sequence $5,0,-5,\_,\_,$, they are $-15,-20$. But I didn't ...
0
votes
1answer
28 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 ...
0
votes
3answers
39 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 ...
-1
votes
1answer
91 views

Find the pattern sequence

I'm trying to help my grandchild with $6$th grade math homework. The question given is: $$ 3.5,\ \ 13,\ \ 41.5,\ \ 127, \cdots $$ What are the next $3$ numbers?
0
votes
3answers
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!
0
votes
1answer
27 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
votes
3answers
74 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 ...
5
votes
3answers
348 views

figuring out an integer function

$f(1) = 1\\ f(2) = 2\\ f(3) = 6\\ f(4) = 20\\ f(5) = 70\\ f(6) = 252\\ f(7) = 924\\ f(8) = 3432\\ f(9) = 12870$ Then what is $f(n)$ (where $n > 0$)? I though about many many possibilities but ...
3
votes
2answers
271 views

Finding the general formula of a sequence: $3,8,23,68,203,608,\cdots$

I have the following sequence : $$3,8,23,68,203,608,\cdots$$ I have found that definition by recurrence of this is $$a(n)=3a(n-1)-1$$ where $a_0=3$ as the first term. I want to find the explicit ...
0
votes
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 ...
2
votes
1answer
82 views

Is this a valid visualization of Euler's identity as a more generic pattern?

I was reading this nice question about a demonstration of Euler's identity, and tried to visualize how would look the left part of the identity in the complex plane by using the following function: ...
1
vote
0answers
18 views

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 ...
1
vote
1answer
44 views

Understand about maximum a posteriori probability (MAP) in classfication task

I have a 2D image defined on a region $\Omega$. Let $I: \Omega \to R$ be a gray image. Assume that the region can be separated into $N$ sub-regions $\Omega_i$ such that $$\forall i,j=1... N:\Omega_i ...
0
votes
0answers
35 views

What is the Sequence?

for n when n is 1 then it gives 2 n is 2 then it gives 4 n is 3 then it gives 7 n is 4 then it gives 11 How do I write this sequence in equation form?
1
vote
1answer
72 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 ...
22
votes
2answers
329 views

What is this pattern found in the first occurrence of each $k \in \{0,1,2,3,4,5,6,7,8,9\}$ in the values of $f(n)=\sqrt{n}-\lfloor \sqrt{n} \rfloor$?

Learning how to generate the Mandelbrot set, I came across the definition of the "escape condition" which is the one that decides the color that is applied to each point of the plane where the ...