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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12
votes
4answers
1k 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 $\ \ \ \ \ \ \ ...
-4
votes
2answers
589 views

How many pairs of integers $(A, B)$ are there in the range $[1,\ldots, N]$, such that $\gcd(A,B) = B$?

I am given a positive integer $N$ ($N\leq 10^9$). How many pairs of integers $(A, B)$ exist in the range $[1,\ldots, N]$ such that $\gcd(A,B) = B$?
0
votes
3answers
1k views

Extract a Pattern of Iterated continued fractions from convergents

I have been working on an article at https://oeis.org/wiki/Table_of_convergents_constants where I posted a table of "convergents constants" (defined at https://oeis.org/wiki/Convergents_constant) ...
0
votes
1answer
225 views

Find the next number in this sequence

I have a homework. It seems to be an easy sequence but I can't get the answer. So, What is the next element? $$2, 7, 10, 13, 23, 34,?$$ What would be the solution out of these numbers? 45 or 49 or 58 ...
37
votes
18answers
10k 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 ...
6
votes
2answers
332 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?
5
votes
0answers
141 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
1answer
1k 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 ...
1
vote
3answers
2k views

What is the next picture in this sequence?

I was reading a book on logical reasoning and came across the following: Can anyone give me the answer to the question. We want the next sequence ?
18
votes
9answers
3k views

Is the Look and Say Sequence a “proper” maths problem? [closed]

I once told my brother about the "Look and Say Sequence" (i.e. 1, 11, 21, 1211, 111221, ...). My brother then showed the sequence to his maths teacher at school and asked him to predict the next ...
6
votes
6answers
357 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 ...
1
vote
1answer
187 views

Patterns of no formula.

How do I find the next number if the given pattern is $$1,2,3,2,3,4,1,2,6,23,14,19,64,69,12,78,152,93,108,?$$ (Find the question mark)
2
votes
1answer
674 views

Bottom to top explanation of the Mahanalobis distance?

I'm studying Pattern recognition and statistics and almost every book I open on the subject I bump into the concept of Mahanalobis distance. The books give sort of intuitive explanations, but still ...
3
votes
3answers
183 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 ...
2
votes
1answer
116 views

Pattern finding for repeating sequences

Find a pattern for the following sequence. 1,1,3,1,3,5,7,1,3,5,7..... Let n= the nth number. Find the nth number of this series
1
vote
3answers
380 views

Patterns in Sequences

I've heard in a movie that for any sequence of numbers, there is a nice formula for generating that sequence. So, for example if I write: 1,2,1,2,3,3,1,2,3,1,2,4,... There is a formula for ...
0
votes
2answers
66 views

Evaluate an unknown operator

I have a simple question but I can't seem to be able to solve it. Given that: 25 ╧ 17 = 267 35 ╧ 23 = 373 45 ╧ 15 = 465 what is ...
0
votes
0answers
355 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