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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-4
votes
1answer
24 views

Find the rule/ formula that creating following linear digit sequence [on hold]

Find the rule/ formula that creating following linear digit sequence using particular formula or linear equation digit sequence is advancing, we need to find out that formula. Given sequence could be ...
0
votes
1answer
11 views

Triangular pyramid. Find the sum of certain numbers on pyramid.

Given that the set of natural numbers continue in the triangular pattern shown below, find the sum of the 6th number in row 7 and the 9th number in row 10. Note: Row 1 is the first row of the ...
0
votes
1answer
44 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
vote
2answers
27 views

General Term of a given series , Where $\sum^{n}_{r=1}U_r=\frac{3n}{2n+1}$

General term $U_r $ of a given series , Where $$\sum^{n}_{r=1}U_r=\frac{3n}{2n+1}$$ I can evaluate that $$ U_1=\frac{3}{3}$$ $$ U_2=\frac{1}{5}$$ $$ U_3=\frac{3}{35}$$ $$ U_4=\frac{1}{21}$$ $$ ...
1
vote
1answer
61 views

Maths Puzzle!!! [duplicate]

I am planning on taking an interview in the near future and was practicing on some previously asked aptitude questions. During my prep I came across a problem for which I couldn't find an answer. ...
-1
votes
1answer
66 views

Next term in the given series

What will be next term of given series: $$​50, 30, 40, 75, 170, ?$$ I am not able to find the pattern in the series. Could someone help me with this?
5
votes
2answers
101 views

Why does this pattern occur when using modular arithmetic against set of prime numbers?

I have been recently playing around with number theory and going through the project Euler problems. So I am very new to a lot of these things. I apologize for not knowing how to look up my answer. ...
0
votes
2answers
57 views

Inductive reasoning question

Can someone help with this inductive reasoning question. What should come next in this series of 5 and what is the reasoning? Can someone also help with the following question.
0
votes
2answers
26 views

Finding a pattern regarding perfect cubes.

For the purpose of this question and the patterns pointed out, $0$ is not a perfect square (some think it is, others no). The first perfect squares are $1$, $4$, $9$, $16$, $25$ and so on. The ...
1
vote
1answer
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 ...
3
votes
2answers
330 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 ...
3
votes
2answers
105 views

What is the $2012th$ number in this pattern?

This is question 30 from Australian Maths 2012 $(0,1,2,1,2,3,2,3,4,1,2,3,2,3,4,3,4,5,2,3,4,...)$ What is the $2012th $ number in this list? What I did: I broke up the first few numbers into ...
1
vote
1answer
52 views

How do I identify pattern of different bases? For example, base $3$? [closed]

Recently,I asked a question on number patterns.Turns out it wasn't the usual number pattern question.It was the sum of the digits at base 3. How do I identify such number patterns or even know that ...
0
votes
1answer
581 views

Pattern matching questions

I saw the below questions and was curious regarding the logic behind the answer. I will be grateful is some one could help me So the question is given the patter, identify the next one
0
votes
1answer
48 views

What is the pattern of the sequence? [closed]

I am currently working at a math camp filled with tiny math geniuses, and one of them gave me a problem yesterday with which I am having trouble. This problem was written by a fourth grader and has ...
8
votes
2answers
246 views

Limit of the sequence $a_{n+1}=\frac{1}{2} (a_n+\sqrt{\frac{a_n^2+b_n^2}{2}})$ - can't recognize the pattern

Consider the sequence: $$a_0=x,~~~b_0=y$$ $$a_{n+1}=\frac{1}{2} \left(a_n+\sqrt{\frac{a_n^2+b_n^2}{2}} \right),~b_{n+1}=\frac{1}{2} \left(b_n+\sqrt{\frac{a_n^2+b_n^2}{2}}\right)$$ $$\lim_{n \to \...
-1
votes
1answer
35 views

How to find a pattern

I have a list of objects. Each object has $3$ values that will have a value from $0$ to $100$. I want to know how iI be able to find the pattern that is most common in that list. Object 1: 1-2-3 ...
0
votes
2answers
60 views

Find the missing Item in the sequence [closed]

There is a sequence described below.What is the missing item? $5,10,?,50,122,...$
-5
votes
2answers
74 views

What is the next Item in the series [closed]

There is a sequence described below.What is the missing item 0,7,26,63,?,...
2
votes
0answers
37 views

Pattern involving squares, primes, and remainders

I ran across a really neat pattern, wholly by accident. In advance, my questions are: Has this been discovered before? If so, where can I learn more about it? Why does this pattern work? Now for ...
0
votes
1answer
13 views

Finding a unique point in a histogram that can be determined even if the histogram is circularly shifted.

Circularly shifted histogram: Modular addition (or subtraction) of a constant value to all data points. Maxima, Minima, etc. might not be a unique value, therefore can't be used. Edit: Let me ...
21
votes
5answers
17k views

How is this a number sequence $58, 26, 16, 14, 10$

I recently had a IQ Test taken and we all got stuck on the same question. The question was: What comes next in the following sequence? $$58, 26, 16, 14,\_\_$$ The answer given in the answer sheet ...
1
vote
0answers
19 views

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 ...
0
votes
0answers
41 views

Sticky boots and modular arithmetic: Find the formula!

Suppose a trek begins and on this trek the road is paved by squares with labels on them. The warning sign next to the beginning of the first square, labeled $1$, states: Beware that due to natural ...
1
vote
1answer
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 ...
10
votes
2answers
323 views

Closed form for $ S(m) = \sum_{n=1}^\infty \frac{2^n \cdot n^m}{\binom{2n}n} $ for integer $m$?

What is the (simple) closed form for $\large \displaystyle S(m) = \sum_{n=1}^\infty \dfrac{2^n \cdot n^m}{\binom{2n}n} $ for integer $m$? Notation: $ \dbinom{2n}n $ denotes the central binomial ...
4
votes
3answers
2k views

Notation for factorial-type pattern with a skip/step of two instead of one?

I came across a peculiar pattern when solving a recurrence relation today: Some sequence $a_n$ looks as such: $a_0 = 1$ $a_2 = \frac{1}{2 \cdot 1}$ $a_4 = \frac{1}{4 \cdot 2 \cdot 1}$ $a_6 = \...
0
votes
2answers
87 views

Can't find the pattern [closed]

These are two sequences: I tried looking for a ratio or difference but it wasn't working $$ 12,20,32,\underline{\quad},22,\underline{\quad},50 $$ $$ 6,10,16,8,\underline{\quad},22\underline{\quad} $$...
2
votes
0answers
239 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 ...
0
votes
1answer
49 views

Pattern finding algorithms

I am working on a server that will update a list each day. The list will look like the following example. ...
0
votes
2answers
34 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
votes
1answer
29 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 ...
4
votes
4answers
17k views

Finding formula for the nth partial sum

A few days ago, I asked for some clarification about pattern recognition and the n-th partial sum for infinite series. Although the explanation given was top-notch (thanks again), I'm still having ...
3
votes
1answer
46 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 ...
10
votes
3answers
19k views

Predict next number from a series

Which methods I can use to predict next number from a series of numbers ? I know the min & max possible number in advance.
0
votes
0answers
9 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
votes
1answer
50 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
votes
1answer
29 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 nk=\frac{...
0
votes
1answer
20 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 ${n \choose k}$ = ($\frac{n}{1}$)($\frac{n-1}{2}$)($\frac{n-...
3
votes
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}, \underbrace{\frac{\...
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
1answer
69 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:           &...
2
votes
5answers
604 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 ...
0
votes
0answers
21 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
vote
0answers
88 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 ...
29
votes
8answers
3k 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 odd....
2
votes
1answer
83 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: ...
5
votes
1answer
168 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 $\frac{K'}{K}...
0
votes
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?
1
vote
1answer
46 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 ...