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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59
votes
7answers
6k views

What's next in this number series? [closed]

340, 680, 1428, 3141.6, _____ This is from an aptitude test. I'm not able to find any pattern in them.
45
votes
4answers
4k views

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 ...
38
votes
18answers
12k views

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 ...
37
votes
5answers
6k views

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 ...
28
votes
7answers
2k 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 ...
19
votes
2answers
1k views

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 ...
12
votes
4answers
2k views

How to solve this sequence $165,195,255,285,345,x$

This is a question appeared in a competitive exam. The question is: Find the unknown term in $165,195,255,285,345,x$ 1)375 $\ \ \ \ \ \ \ \ $ 2)420 3)435 $\ \ \ \ \ \ \ ...
12
votes
3answers
616 views

Consecutive Prime Gap Sum (Amateur)

List of the first fifty prime gaps: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4. My ...
11
votes
3answers
200 views

Digital root of twin prime semiprimes

It appears that the product of any pair of twin primes (excluding the first pair 3 and 5) yields a semi prime whose digital root is equal to $8$. Example: $$ 17 \cdot 19 = 323 $$ The digital root of ...
10
votes
2answers
205 views

Has anyone noticed this pattern?

I've been messing around a bit and I noticed a curious pattern when it comes to progressions of powers. Let's take the progression of consecutive integers: $1,2,3,4,5,6,7,...$ Obviously it's an ...
9
votes
7answers
4k views

Pattern to last three digits of power of $3$?

I'm wondering if there is a pattern to the last three digits of a a power of $3$? I need to find out the last three digits of $3^{27}$, without a calculator. I've tried to find a pattern but can not ...
8
votes
2answers
138 views

Finding pattern

Just a puzzle. \begin{matrix} 2 & 9 & ? \\ 11 & 33 & 66 \\ 8 & 3 & 27 \\ \end{matrix} The options are $35$, $40$, $45$, $55$. $45$ is false. I ...
7
votes
3answers
814 views

How to find pattern in $1,2,8,9,15,20,26,38…$ infinite sequence?

While I was investigating some specific types of prime numbers I have faced with the following infinite sequence : $1,2,8,9,15,20,26,38,45,65,112,244,303,393,560,....$ I tried to find recursive ...
7
votes
1answer
92 views

Finding $x^n$ patterns

I noticed the other day while computing consecutive powers of $2$ that for $n \geq 1$, the numbers in the ones place of the values of $2^n$ repeat every 4 terms $(2, 4, 8, 6,\ldots)$. In the tens ...
7
votes
1answer
223 views

What is the pattern or relation in this table?

Here is the table: $$\begin{array}{c} 0\\ 1\\ 1& 1\\ 3& 2& 3\\ 5& 3& 3& 5\\ 11 &8 &10 &8 &11\\ 21 &13 &14 &14 &13 &21\\ 43 ...
7
votes
1answer
376 views

How to Characterize Clumps in a Large, Semi-Random Graph

Consider large (100,000+ vertices, say) graphs, which we think of as representing some population with edges representing some form of symmetric relation. They might be the Friend graph of Facebook, ...
6
votes
2answers
354 views

Formula to this pattern?

I have this pattern: 1 11 21 1211 111221 I'm guessing it's a fibo pattern, been at it for hours now. Anyone know?
6
votes
6answers
418 views

Do the differences of perfect squares apply to perfect cubes and more?

I'm curious about a special property of squares. The difference between perfect squares starting from 0 are 1,3,5,7,9..., where each difference goes up by 2. I want to know if there are any patterns ...
6
votes
1answer
225 views

Fractals - when the number of seed shapes that can fit into the scaled-up copy is non-integer.

I've heard people say (for eg. here) that the dimension of fractal patterns (particularly, in this question, Lindenmayer fractals) can be formulated as follows: $$D=\frac{\ln N}{\ln S}$$ Where $N$ ...
6
votes
2answers
297 views

Permutations to satisfy a challenging restriction

In a stack of n distinct cards in order {1,2,3,4,...,n} from top, define distance between 2 cards as the number of cards between them. 2 cards are neighbours if they're adjacent in original ...
5
votes
3answers
936 views

Recognizing the sequence 1/16, 1/8, 3/16, 1/4, 5/16, …

What is the missing number? $$\frac{1}{16}, \frac{1}{8}, \frac{3}{16}, \frac{1}{4}, \frac{5}{16}, \ \ \ [?]$$ $$A. \frac{5}{4}\quad B. \frac{3}{4}\quad C. \frac{5}{8}\quad D. \frac{3}{8}$$ ...
5
votes
2answers
258 views

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 ...
5
votes
0answers
67 views

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 ...
5
votes
0answers
113 views

Find the number that follows the rules of two different series

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. $$ ...
5
votes
0answers
157 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 $D_2$
4
votes
3answers
1k 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 = ...
4
votes
1answer
2k 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 ...
4
votes
3answers
106 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 ...
4
votes
1answer
121 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 ...
4
votes
2answers
42 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 ...
4
votes
1answer
177 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 ...
4
votes
2answers
64 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 ...
4
votes
0answers
118 views

Adding Numbers Pattern

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 ...
3
votes
1answer
147 views

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 ?
3
votes
3answers
368 views

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 ...
3
votes
3answers
9k 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
3answers
109 views

Is there any pattern to pythagorean triples where there are two a-b pairs for one c?

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, ...
3
votes
1answer
194 views

Possible Prime Sum Pattern (Amateur)

Disclaimer: I’m an amateur, and have no advanced knowledge of math, so please forgive my ignorance as I’m just curious to know if I’ve stumbled upon something or not. Prime Numbers: 2, 3, 5, 7, 11, ...
3
votes
2answers
106 views

Recognize a valid binary Golay codeword

Are there any properties of a binary [24,12,8] Golay code which would allow me to say, for example, that a given 24-bit word is or is not a Golay codeword for some generator matrix? That is to say, is ...
3
votes
1answer
101 views

Consecutive Prime Problem

Consecutive primes whose quotient of their product and sum is itself a prime number. $$ 2 \times 3 \times 5 = 30 $$ $$ 30/10 = 3 $$ $$ 3 \times 5 \times 7 = 105 $$ $$ 105/15 = 7 $$ Question: ...
3
votes
1answer
138 views

Get N value of this pattern (Triangular Number)

I have numbers formatted into this pattern. $$ ...
3
votes
1answer
71 views

finding all pairs $(x,z)$

How to find all pairs $(x,z)$ of integers for which $2(z+1)^3$ is divisible by $xz-1$
3
votes
3answers
218 views

Using Correlation for mouse gesture recognition

I am in need to build a mouse gesture recognition system which will compare given recognition to the the gestures in training data and will say where a given gesture best fits. I am planning to use ...
3
votes
0answers
438 views

Guilloché security printing — can it be cracked?

Money uses Security printing, and often uses Guilloché patterns. These curves are inscribed by wheels on wheels on wheels, ten wheels deep in some cases. For example, the back of the US $1 bill has ...
3
votes
0answers
247 views

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 ...
3
votes
0answers
440 views

What does this say about prime numbers?

I was having fun with Sage when I noticed something interesting: ...
2
votes
2answers
398 views

Prime Number Sum Sequence (Amateur)

SOLVED: This is false Beginning with 3, add the next consecutive prime (2) and then take that sum (5) and add that to next consecutive prime (3) to get (8), and so on... $$ 3 + 2 = 5 $$ $$ 5 + 3 = 8 ...
2
votes
2answers
102 views

Finding pattern- $6$ $11$ $25$

Finding pattern$$ \begin{matrix} 6 & 11 & (25) \\ 8 & 6 & (16) \\ 12 & 5 & (?) \\ \end{matrix} $$ Options are : $10/12/14/16$ My ...
2
votes
1answer
153 views

Mathematical formula for a pattern

I was cooking and saw a chart of temperature vs cooking time like so: $154\mathrm{F}$ - $36$ hours $164\mathrm{F}$ - $18$ hours $174\mathrm{F}$ - $9$ hours Basically for every $10\mathrm{F}$ ...
2
votes
4answers
128 views

Pattern Recognition - How to solve this problem? [closed]

A general term of the sequence $$ -8,-7,-10,-1,-28,53,\ldots $$ can be expressed as $\dfrac{a-b^{n-1}}{4}$, where $a$ and $b$ are integers. What is the value of $ab$? Teach me how to solve this ...