# 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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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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: ...
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### 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 ...
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### 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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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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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) ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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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### 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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### 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.