# Tagged Questions

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### 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: ...
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### Why is $A_1 x + … + A_n x^n$ a solution of $\sum_0^{n} (-1)^n \frac{x^n}{n!} \frac{d^n y}{d x^n} = 0$?

I was playing(/fiddling) around with some maths and I saw this pattern( where $A_n$ is a constant.): $A_1 x$ is a soultion of: $$\frac{y}{x} - \frac{dy}{dx} = 0$$ $A_1 x + A_2 x^2$ is a ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### What makes a pattern in a sequence?

Assume a stream of characters$(c)$ where $c \in (A, B, C ... Z)$. I need to identify patterns available in the stream. As per the definition of a pattern I should be looking for a recurring string. ...
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### How to represent the $n$th number in the sequence $1,3,5,7,1,3,5,7,\dots$ as a closed form?

I'm given the repeating sequence $1,3,5,7,1,3,5,7,\dots.$ I must determine a formula for the $n$th term of the sequence. I have tried the triangle method, but since this is a repeating series it is ...
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### 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
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### 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 $\gcd(A,B) = B$?
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### Finding a generating function for a pattern

I was working on this projecteuler.com problem, and I was very interested by the premise. Essentially, given n terms, find an ...
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### Find n term of sequence

A sequence is given: $$1,10,11,100,101,110,111,1000,\dots,a_n,\dots$$ The question is: what is the value of $a_n$ for a given $n$? I have tried a lot of patterns but was not able to meet the ...
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### Calculation for absolute value pattern

I have a weird pattern I have to calculate and I don't quite know how to describe it, so my apologies if this is a duplicate somewhere.. I want to solve this pattern mathematically. When I have an ...
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### Finding $n^{th}$ term of sequence

$$3,8,17,32,57,\ldots$$ How do we find the $n^{th}$ term? I have been roaming aimlessly for a few minutes now. A definite pattern is in the differences of differences. Hints will be apreciated.
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### How to calculate a result based on an exponentially changing pattern/sequence. [duplicate]

Given any number (including decimals) between 12.5 and 87.5 I need to calculate another number based on these results:  Input = 12.5 | 31.25 | 50 | 68.75 | 87.5 Result = 12.5 | 64.5  | 78 | ...
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### 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 ...
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### Understanding the fundamentals of pattern recognition

I'm learning now about sequences and series: patterns in short. This is part of my Calc II class. I'm finding I'm having difficulty in detecting all of the patterns that my text book is asking me to ...
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### Guess the terms in the sequence?

I am writing GRE in 2 two months, and I just can't solve these sequence question. Can anyone tell what the missing terms are and what is the pattern here? Find the next 4 terms in this sneaky ...
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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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### How to find the pattern?

I'm challenging myself to figure out the mathematical expression of the number of possible combinations for certain parameters, and frankly I have no idea how. The rules are these: Take numbers ...
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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 ...