Questions tagged [sequence]
For challenges involving sequences, typically of numbers following some pattern.
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Find the longest permutations of integers from 1..k such that all neighbouring pairs sum to a square
OEIS A090461 details the ‘numbers k for which there exists a permutation of the numbers 1 to k such that the sum of adjacent numbers is a square’. This has also been the subject of Matt Parker’s ...
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Numbers with distinct decimal digits
Write a program or function that outputs all positive integers with distinct decimal digits (OEIS: A010784)
Examples:
...
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Golf the fast growing hierarchy
The fast growing hierarchy is a way of categorizing how fast functions are growing,
defined the following way (for finite indices):
\$ f_0(n)=n+1 \$
\$ f_k(n)=f_{k-1}^n(n)\$ with \$f^n\$ meaning ...
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How Many Staircases [duplicate]
Problem
You're a staircase engineer on a house and realize you only have n rectangles to create a staircase. So you are tasked with finding the number of ways to ...
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Otteretto Classic game scoring method
Brief description of the game
In the game Otteretto Classic (which you can test directly in your browser; try it!) the player has to form palindromic sequences using adjacent cells on a square grid. ...
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Piecing Paired Primes
Problem
You've stumbled upon a paradoxical mathematical phenomenon related to prime numbers. Consider the following scenario:
You have an infinite list of prime numbers: $$2, 3, 5, 7, 11, 13, 17, 19, ....
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Give the fool's Fibonacci sequence
Recently I asked for tips on improving some code-golf of mine. The code was supposed to output every third value of the Fibonacci sequence starting with 2:
...
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Encrypting Emojis
Problem
You are tasked with creating a program that performs emoji encryption on a given string of emojis. In this encryption scheme, each emoji is replaced by a unique character (from ...
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Output the smallest increasing sequence where each term is coprime to preceding 3 terms
This sequence is defined as
Starts with 1, 2, 3
The next element of the sequence is the first number greater than the previous three that is co-prime with each of the previous 3 elements in the ...
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Magic OEIS formulae (Robbers' thread)
This is the robbers' thread. See the cops' thread here.
In this cops and robbers challenge, the cops will be tasked with writing an algorithm that computes some function of their choice, while the ...
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Magic OEIS formulae (Cops' thread)
This is the cops' thread. See the robbers' thread here.
In this cops and robbers challenge, the cops will be tasked with writing an algorithm that computes some function of their choice, while the ...
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The all-high powerful numbers
We've had powerful numbers, yes, but what about highly powerful numbers?
Highly powerful numbers
Let \$n\$ be a positive integer in the form
$$n = p_1^{e_{p_1}(n)}p_2^{e_{p_2}(n)}\cdots p_k^{e_{p_k}(n)...
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Repeating occupied pattern in Hilbert's hotel
Imagine a countable infinite amount of empty rooms. When an infinite amount of guests come, they occupy the 1st, 3rd, 5th...(all odd) empty rooms. Therefore there's always an infinite amount of empty ...
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Make a k-skip-j range
On the Mathematica Stack Exchange, 100xln2 asks:
I need a list of integers […] The list contains integers and is characterized by [three] parameters, lets call them k and j [and listmax], which ...
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Print all Polynomials
The set of all polynomials with integer coefficients is countable.
This means that there is a sequence that contains each polynomial with integer coefficients exactly once.
Your goal is it to write a ...
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Numbers that can be negated by reading backwards
Balanced ternary is a modified version of ternary (base 3), using the three digits 1,0 and -1...
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Sum of a range of a sum of a range of a sum of a range of a sum of a range of a sum of
Inspired by the fact that a few related challenges to this could be answered by Vyxal in 0 Bytes using a special flag combination.
Given only one input integer \$n\$, calculate \$f(n,n)\$ where
$$ f(x,...
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Compute the maximal Ducci period
Given an initial \$n\$-tuple \$t_0=(t_{0,1},...,t_{0,n})\$, we can obtain its corresponding Ducci sequence \$\{t_0, t_1, ...\}\$ by the recurrence \$\displaystyle t_{i+1}=\left(\left|t_{i,1}-t_{i,2}\...
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Generate all linked chains
A followup to this challenge by Jeremy Collprav, inspired by DLosc solving this in Regenerate. Some sections copied from the linked challenge.
Linking chains
We define a chain to be a string ...
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Last odd digit of power of 2
Task
Given \$n\$, output position of the last odd digit in the decimal representation of \$2^n\$ (counting from the end).
Rules
There are no odd digits for \$n=1,2,3,6,11\$ \$(2, 4, 8, 64, 2048)\$ - ...
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Lowest digit addition generator
A digit addition generator of an integer n is any integer x that satisfy the equation ...
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How many sorting networks?
Below on the left is a picture of a sorting network that can sort 4 inputs. On the right you can see it sorting the input 3,2,4,1.
A sorting network of size ...
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Straight pen strokes for Prime Numbers
Challenge
You are supposed to output the series I recently designed which goes as follows which are pen stroke counts of ascending prime numbers:
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Hankel transform of an integer sequence
A Hankel matrix is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.:
$$\begin{bmatrix} a & b & c & d \\ b & c & d & e \\ c & d &...
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The number of solutions to Hertzsprung's Problem
Hertzprung's Problem (OEIS A002464) is the number of solutions to a variant of the Eight Queens Puzzle, where instead of placing \$n\$ queens, you place \$n\$ rook-king fairy pieces (can attack like ...
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Enumeration of free polyominoes
A polyomino with \$n\$ cells is a shape consisting of \$n\$ equal squares connected edge to edge.
No free polyomino is the rotation, translation or reflection (or a combination of these ...
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Doors and guards
Related but noticeably different
You are the leader of the guard in the dungeon of an ancient castle.
There are N doors in the dungeon and ...
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Record Least Uncommon Multiple Counts
The Greatest Common Divisor, or gcd, of two positive integers \$x\$ and \$y\$ is the largest positive integer that divides both \$x\$ and \$y\$.
The Least Common Multiple, or lcm, of two positive ...
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Largest Binary Area
Take the sequence of all natural numbers in binary, (1, 10, 11, ..) then write them vertically beside each-other like this (least significant bit on top; 0s have ...
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Bumping Series Implementation
I have a follow-up question here from my previous question on Math SE. I am lazy enough to explain the content again, so I have used a paraphraser to explain it below:
I was considering arbitrary ...
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Primes with Distinct Prime Digits
There are 18 primes with distinct prime digits (A124674). Namely, they are:
\$2, 3, 5, 7, 23, 37, 53, 73, 257, 523, 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523\$
Your task is to output this ...
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Fibonacci Binary Squares
I was playing with the Fibonacci sequence in binary like so (note that the binary representations are written here from smallest bit to largest bit):
...
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A Fine sequence with fine interpretations
The ubiquitous Catalan numbers \$C_n\$ count the number of Dyck paths, sequences of up-steps and down-steps of length \$2n\$ that start and end on a horizontal line and never go below said line. Many ...
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Approximate a root of an odd degree polynomial
Every odd degree polynomial has at least one real root. However this root does not have to be a rational number so your task is to output a sequence of rational numbers that approximates it.
Rules
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Print all pandigital numbers
Given a base as input, output all pan-digital numbers. A number is pan-digital if it includes every digit in that base at least once, possibly multiple times. Every number is considered to contain an ...
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Distance to the average of the next two prime numbers
Suppose we have a sequence \$P\$. Every element \$P_n\$ represents the distance between the \$n^{th}\$ prime number and the average of the next two prime numbers.
For example, \$P_1\$ would be the ...
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Don't repeat yourself
In this challenge you will be tasked with implementing a sequence of natural numbers such that:
Each number appears a natural number of times
No two numbers appear the same number of times
No two ...
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Smallest Bit Rotation
For a given positive integer, try to find out the smallest possible rotation resulted by rotating it 0 or more bits.
For example, when the given number is 177, whose binary representation is \$...
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Keep elements in sequence that have a letter repeated at least 3 times
Challenge:
Given the input array l with a list of strings, only keep the elements in the sequence that have a letter that's repeated at least 3 times. Like ...
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Create \$n\$ sublists with the powers of two (1, 2, 4, 8, 16...)
Challenge:
Given the input number n. It should give me nested sublists of n layers with the power of two numbers for each level. ...
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CGAC2022 Day 16: Playing with bits, Part 2
Part of Code Golf Advent Calendar 2022 event. See the linked meta post for details.
As soon as the Elves get bored with the last week's game, Bin comes up with a new game. The rules are similar, ...
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CGAC2022 Day 9: Playing with bits
Part of Code Golf Advent Calendar 2022 event. See the linked meta post for details.
The Elves like playing number games. One day, Bin (a friend of Fen) suggests a new game: given a positive integer <...
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CGAC2022 Day 3: \$n\$-dimensional Chocolate Pyramid
Part of Code Golf Advent Calendar 2022 event. See the linked meta post for details.
I've got an infinite supply of \$n\$-dimensional chocolate for some positive integer \$n\$. The shape of the ...
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Find the nth number where the digit sum equals the number of factors
(This is OEIS A057531.)
Your task
Given a positive integer, \$n\$, find the \$n\$th number where the digit sum equals the number of factors
Explanation
For example, let's take 22:
Its factors are \$[1,...
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"Prime" pyramid
The pyramid begins with the row 1 1. We'll call this row 1. For each subsequent row, start with the previous row and insert the current row number between every ...
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Power sequence differences
Your task
Given two positive integers \$x\$ and \$d\$ (such that \$d<x\$), output the 5th term of the \$d\$th difference of the sequence \$n^x\$
Example
Let's say we are given the inputs \$x=4\$ ...
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Length of Binary as Base 10 [OEIS A242347]
Computers like binary. Humans like base 10. Assuming users are humans, why not find the best of both worlds?
Your task is to find the first n terms in the sequence ...
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Looking back at all the things I said ...
The look-say sequence is a sequence of lists of numbers where each element is the previous element with run length encoding. Run length encoding is the process of grouping together like elements and ...
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Enumerate the rationals
The cardinality of the set \$\mathbb Q\$ of rational numbers is known to be exactly the same as that of the set \$\mathbb Z\$ of integers. This means that it is possible to construct a bijection ...
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Generate the n'th Fermi-Dirac Prime
A Fermi-Dirac Prime is a prime power of the form \$p^{2^k}\$, where \$p\$ is prime and \$k \geq 0\$, or in other words, a prime to the power of an integer power of two. They are listed as integer ...
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