# Questions tagged [sequence]

For challenges involving sequences, typically of numbers following some pattern.

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### Print this sequence I just made up

To get this sequence I just made up, which will subsequently be referred to as TSIJMU, consider the harmonic series: $\frac{1}{2} + \frac{1}{3} + \frac{1}{4} ...$ But what if you only add a term if ...
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### Elevator sequence

Totally not inspired by Lyxal repeatedly mentioning elevators in chat :P Challenge In short: simulate some people filling up an elevator and then leaving it. The elevator is simplified as a grid, ...
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### Outputting Blum Integers

According to Wikipedia, In mathematics, a natural number $n$ is a Blum integer if $n = p \times q$ is a semiprime for which $p$ and $q$ are distinct prime numbers congruent to $3 \bmod 4$. ...
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### Largest Number with No Repeating Digit Pairs

Inspired by the problem with the same name on Puzzling SE by our very own Dmitry Kamenetsky. You are to find the largest number that only uses every digit pair once, in a given base. For example, in ...
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### Binomial transform

Background Binomial transform is a transform on a finite or infinite integer sequence, which yields another integer sequence. The binomial transform of a sequence $\{a_n\}$ is given by s_n = \sum_{...
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### Mr. Binary Counterman

Mr. Binary Counterman, son of Mr. Boolean Masker & Mrs. Even Oddify, follows in his parents’ footsteps and has a peculiar way of keeping track of the digits. When given a list of booleans, he ...
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### Code the Levine sequence

Introduction Note that I learned it from a Numberphile Video, where Neil Sloane explains it better. I recommend you to watch his Video. But for a quick Introduction: The Levine Sequence is made from ...
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### Placing circles along a square spiral

In this code golf challenge, you'll be computing the placement of (open) circles of areas $\pi, 2\pi, 3\pi, \dots$ when greedily placed along integer points in a square spiral in such a way that no ...
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### Generalised Fortunate Prime Sequences

The primorial $p_n\#$ is the product of the first $n$ primes. The sequence begins $2, 6, 30, 210, 2310$. A Fortunate number, $F_n$, is the smallest integer $m > 1$ such that $p_n\# + m$ ...
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### Self-Replicating Numbers

Background For the purpose of this challenge, all numbers and their string representations are assumed to be in decimal (base 10). I tried to find proper terminology for this challenge, but I do not ...
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### Sociable sequences

Sociable numbers are a generalisation of both perfect and amicable numbers. They are numbers whose proper divisor sums form cycles beginning and ending at the same number. A number is $n$-sociable ...
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### First sequence with no square differences

Consider the sequence $(a_n)$ defined in the following way. $a_0=0$ For all $n=1, 2, 3, \dots$, define $a_n$ to be the smallest positive integer such that $a_n-a_i$ is not a square number, ...
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### Topologically distinct ways of dissecting a square into rectangles

I was asked by OEIS contributor Andrew Howroyd to post a Code Golf Challenge to extend OEIS sequence A049021. Would be super great to get a couple more terms for [...] A049021. Kind of thing [...] ...
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### Generalise perfect numbers

Let $\sigma(n)$ represent the divisor sum of $n$ and $\sigma^m(n)$ represent the repeated application of the divisor function $m$ times. Perfect numbers are numbers whose divisor sum equals ...
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### Square root multiples

This code-challenge is based on OEIS sequence A261865. $A261865(n)$ is the least integer $k$ such that some multiple of $\sqrt{k}$ is in the interval $(n,n+1)$. The goal of this challenge is ...
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### Count unrooted, unlabeled binary trees of n nodes

An unrooted binary tree is an unrooted tree (a graph that has single connected component and contains no cycles) where each vertex has exactly one or three neighbors. It is used in bioinformatics to ...
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### Merge Two Paragraphs with Removing Duplicated Lines

Challenge The goal of this challenge is to make a function that takes two paragraphs and output a concatenated result with removing the duplicated overlapped lines due to redundancy (but a single copy ...
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