# 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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### What is the logic to the sequence $10$, $2$, $4$, $6$, $2$, $8$, $5$? [on hold]

$$10, 2, 4, 6, 2, 8, 5$$ Can someone tell me the logic behind this sequence? It was a question on a magazine without the last number —$5$— but I can't find any logic.
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### effect of number of samples on performance of unsupervised clustering algorithms

I want to apply a k means classification algorithm on a set of data. How does the performance of the clustering algorithm depend on the number of samples available to it? Specifically, instead of ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### 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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### What is the next Item in the series [closed]

There is a sequence described below.What is the missing item 0,7,26,63,?,...
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### 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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### 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 ...
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### Pattern finding algorithms

I am working on a server that will update a list each day. The list will look like the following example. ...
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### 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. ...
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### 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 ...
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### 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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Let $n$ $\epsilon$ N and let $k$ $\epsilon$ {0,...,n}. Explain why it follows from ${n \choose k}$ = ${n \choose k-1}$$\frac{n-k+1}{k} that {n \choose k} = (\frac{n}{1})(\frac{n-1}{2})(\frac{n-... 2answers 51 views ### I think I've found all roots to f_k(x)=\sum_{j=1}^k x^j-x^{-j} for any k - how to prove it? Conjecture: The set of unique roots of$$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{\... 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 ... 5answers 621 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 ... 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 $$12,20,32,\underline{\quad},22,\underline{\quad},50$$ $$6,10,16,8,\underline{\quad},22\underline{\quad}$$... 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 ... 0answers 89 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 ... 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? 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. 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 ... 0answers 34 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 ... 1answer 107 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 ... 3answers 195 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 ... 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: &... 2answers 135 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. 3answers 75 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) ... 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}...
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, ...