# 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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### Eyebrow-raising pattern of number of primes between terms of the Fibonacci number sequence?

So, $$1,1,2,3,5,8,13,21...$$ Any connection to primes?...it appears not. However, in between the Fibonacci numbers are how much primes? Let's see: 1 and 1 ZERO 1 and 2 NADA 2 and 3 ZILCH 3 and 5 ZIP ...
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### Getting the sequence $\{1, 0, -1, 0, 1, 0, -1, 0, \ldots\}$ without trig?

What's the simplest way to write a function that outputs the sequence: {1, 0, -1, 0, 1, 0, -1, 0, ...} ... without using any trig functions? I was able to come ...
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### If a prime number is reversed, and then appended to itself, why is the result always a composite number?

$2 \Rightarrow 22$ which is a composite number. $37 \Rightarrow 3773$ which is a composite number. $523 \Rightarrow 523325$ which is a composite number. $8123 \Rightarrow 81233218$ which is a ...
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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 odd....
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### 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 ...
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### 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 ...
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### Understanding this pattern behind the Fibonacci sequence

To be honest, I'm pretty awful at mathematics however, when up till 6AM I do like to do random things throughout the night to keep me occupied. Tonight, I began playing with the Fibonacci sequence in ...
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### Is This A Derivative?

I am in a little over my head. This all began with my reading how each level of pascals triangle adds to $2^n$, where n=row# starting with n=0. I then though, "wouldn't it be clever if the rows added ...
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### What Constitutes a Pattern

Mathematics is often referred to as the "study of patterns." What I'm wondering is whether there is somehow a technical way to describe a pattern. For the length of this question let's assume that we'...
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I have this logic problem where I need to find a number that fits in 2 different series (vertical and horizontal). Each series has a rule, and once you find them, you can determine the answer. $$... 0answers 171 views ### Point Group of a pattern I need to determine the point group of the following patterns: I think the one on the left is D_1 and the one on the right is D_2 3answers 2k views ### Notation for factorial-type pattern with a skip/step of two instead of one? I came across a peculiar pattern when solving a recurrence relation today: Some sequence a_n looks as such: a_0 = 1 a_2 = \frac{1}{2 \cdot 1} a_4 = \frac{1}{4 \cdot 2 \cdot 1} a_6 = \... 1answer 3k views ### Find the pattern, What is the correct answer Ok, so this question is from seriously hard IQ test that has been doing the rounds on facebook, ok, 17 questions are easy 3 are hellishly hard, The answer to this one is 17, I do not know why, I found ... 4answers 17k views ### Finding formula for the nth partial sum A few days ago, I asked for some clarification about pattern recognition and the n-th partial sum for infinite series. Although the explanation given was top-notch (thanks again), I'm still having ... 3answers 109 views ### Rewriting exponents as sigmas, is this a thing? Is this a thing? If not, can anyone help me out on this? So I saw this a while back.$$\sum_{i=0}^n(2n + 1) = n^2$$For positve n. This is interesting, and I wondered if I could write any n^x in ... 1answer 137 views ### Some questions about \gcd(n,m) and \phi(n) I was messing around in Excel at the end of work today and made a table where the (i,j) entry a_{i,j}, for j \geq i, is 1 exactly when i and j are coprime (see snapshot of a portion of the ... 2answers 53 views ### formula for number triangles Hi, I have a triangle starting from 0 and going up by one on the bottom row until there are r items on the bottom row and there are r rows a number is formed by adding the two numbers towards ... 1answer 262 views ### the table at the end of Theoretical Computer Science Cheat Sheet Theoretical Computer Science Cheat Sheet, created by Steve Seiden, is a hodgepodge of well-known mathematical theorems and notions. I can understand (or guess at least) many of them, but I'm not sure ... 2answers 93 views ### How to solve linear, second order ODE with Frobenius method with a difficult recurrence relation? The ODE in question is:$$4xy''+2y'+y=0$$Shifting the power series of each term so that they are all raised to the power (n+r) will yield this recurrence relation:$$a_{n+1}={a_n\over (n+r+1)(-2-4(...
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A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
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### Pattern puzzle help

I've spent hours on this puzzle, which shouldn't be too hard, and I'm sure I've got the right answer, but apparently it's wrong. The problem statement: You are guessing a positive number X. You ...
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### What does this say about prime numbers?

I was having fun with Sage when I noticed something interesting: ...
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### What is the Galois group of $x^n + (x-1)^n$?

What is the Galois group of $x^n + (x-1)^n$ over the rationals in terms of the integer $n$ ? In case that is too hard , what is it for the first 20 integers ?
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### 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 ...
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### Largest number on multiplying with itself gives the same number as last digits of the product

What is the largest number on multiplying with itself gives the same number as last digits of the product? i.e., $(376 \times 376) = 141376$ i.e., $(25\times 25) = 625$ If the largest number cant ...
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### Mathematical Background for Computer Vision [closed]

I am a PhD student and would like to do deep research in the area of computer vision and pattern recognition. I know to be successful I need strong mathematical background. Could you please introduce ...
### 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 ...
I've found lots of Pythagorean triples like this, where there are two triples with the same c. Is there any pattern to them $17^2 + 144^2 = 145^2$ $24^2 + 143^2 = 145^2$ examples: (by c) 145, 185, ...