Questions tagged [sequence]
For challenges involving sequences, typically of numbers following some pattern.
819
questions
26
votes
10answers
3k views
The square root of the square root of the square root of the…
This code-golf challenge will give you an integer n, and ask you to count the number of positive integer sequences \$S = (a_1, a_2, \dots, a_t)\$ such that
\$a_1 + ...
18
votes
5answers
520 views
Triangles with rational side lengths
This challenge will have give you a positive integer \$n\$ and ask you to output \$t(n)\$, the number of triangles (up to congruence) satisfying the three conditions:
The triangles have perimeter of ...
17
votes
23answers
2k views
Create an Accurate How-To Article
Here is an easy-intermediate challenge for anyone interested!
What is that?
A thing me and brother do a bit too often is this:
One of us has a problem and asks the other to explain how to do certain ...
23
votes
20answers
1k views
Sequences of distinct positive integers
The goal of this challenge is to take a positive integer n and output (in lexicographic order) all sequences \$S = [a_1, a_2, ..., a_t]\$ of distinct positive ...
24
votes
2answers
1k views
Extend the most recent "nice" OEIS sequence: stepping stone puzzle on a grid
Today Neil Sloane of the OEIS sent out an email asking for a confirmation of the current terms, and computation of some larger terms of the latest OEIS sequence A337663 with the keyword "nice&...
2
votes
0answers
105 views
Grow in a slow-growing sequence [duplicate]
Background
There is an interesting question on MathSE about some conjectures that are disproven by extremely large counter-examples. This delightful answer tells the story of a sequence of numbers ...
22
votes
16answers
2k views
Delicate primes
Inspired by Find the largest fragile prime.
By removing at least 1 digit from a positive integer, we can get a different non-negative integer. Note that this is different to the ...
30
votes
25answers
3k views
Implement the random Fibonacci sequence
The random Fibonacci sequence is defined as follows:
$$
f_n =
\begin{cases}
f_{n-1}+f_{n-2} \text{ with probability } 1/2 \\
f_{n-1}-f_{n-2} \text{ with probability } 1/2 \\
\end{cases}
$$
$$
f_1 = ...
33
votes
83answers
3k views
Lolololololololololololol
Let us take a break from the brain-wrecking questions and answer some of the simpler ones
You have recently read something extremely funny, and want to express your laughter to the world! But how can ...
24
votes
33answers
3k views
Find the largest banknote
Banknotes in many countries come in denominations of 1,2,5,10,20,50,100,200,500,1000, etc. That is, one of \$ \{ 1,2,5\} \$ times a power of \$10\$. This is OEIS A051109, except we'll extend the ...
9
votes
14answers
817 views
Descending dungeons of positional systems
The sequence discussed in this challenge is a variant of the Descending Dungeons sequence family. Specifically, the sequence generation rules:
...
-5
votes
2answers
187 views
Solve the dress problem [closed]
Background
Peter's Father, the Teacher of a dance-club, asks Peter a question:
Given are two natural numbers (\$\mathbb{N}\$ \$x\$ and \$y\$).
\$x\$ is the number of the garment types (e.g. shorts, ...
9
votes
8answers
1k views
10
votes
10answers
2k views
Lumberjaxe Code Golf
Tom the lumberjack is going to do his daily routine: chop trees. After all, it's his job to do so. His boss has ordered him to chop trees in a straight line marked with a special tape to identify them,...
5
votes
8answers
264 views
Is it a geometric sequence or not? [closed]
Well, last time I asked for an arithmetic sequence, now comes the geometric sequence
Challenge
In this challenge, the input will be an unordered set of numbers and the program should be able to tell ...
-7
votes
4answers
226 views
Is it an Arithmetic Sequence or not? [closed]
Challenge
In this challenge, the input will be an ordered set of numbers and the program should be able to tell if the set of numbers is an Arithmetic Sequence.
Input
The input will be a list ...
12
votes
3answers
767 views
Metagolf the OEIS
We've had Meta Regex Golf and Display OEIS Sequences. Now, it is time for Meta OEIS Golf.
Challenge
Given a sequence of integers, your program/function should output a program/function in the same ...
12
votes
3answers
282 views
Friendly Incenters
The incenter of a triangle is the intersection of the triangle's angle bisectors. This is somewhat complicated, but the coordinate formula for incenter is pretty simple (reference). The specifics of ...
14
votes
5answers
648 views
Placing Dominoes On A Chequerboard
How many ways can one place (unlabelled) dominoes on a square chequerboard such that the number placed horizontally is equal to the number placed vertically?
The dominoes must align with, and may not ...
24
votes
23answers
2k views
Complete a sequence using its distances
Given \$A = (a_1,\dots,a_k)\ k\ge2 \$ a sequence of positive integers, in which all elements are different.
Starting from \$i=2\$, while \$a_i\in A:\$ (until the last element)
If \$d=|a_i-a_{i-1}|\$ ...
12
votes
10answers
902 views
Find all Belphegor primes
A Belphegor number is a number of the form \$(10^{n+3}+666)*10^{n+1}+1\$ (1{n zeroes}666{n zeroes}1) where \$n\$ is an non-negative integer. A Belphegor prime is a ...
9
votes
3answers
485 views
Number of tilings on a triangular board with triangular tiles
Background
Consider the shape \$T(n)\$ consisting of a triangular array of \$\frac{n(n+1)}{2}\$ unit regular hexagons:
John Conway proved that \$n = 12k + 0,2,9,11\$ if and only if \$T(n)\$ can be ...
11
votes
3answers
502 views
Triangles in a tetrahedron
The goal of this challenge is to extend the OEIS sequence A334581.
Number of ways to choose \$3\$ points that form an equilateral triangle from the \$\binom{n+2}{3}\$ points in a regular tetrahedral ...
12
votes
10answers
2k views
24
votes
11answers
2k views
Generate A065825
(This is A065825.) The sequence defaults apply, so you can pick another format other than this one.
Given an input integer n, find the smallest number ...
12
votes
3answers
511 views
How much weight can you lift?
With all the gyms closed down with the COVID-19 situation, we have to exercise with the weight we have lying around at home. The problem is, we have a small selection of plates at varying weights, and ...
22
votes
15answers
2k views
Donation arms race
The barfoos, a hypothetical alien species, go about charity in an interesting way.
Every morning, barfoo Specialists come up with an ordered list of causes to donate to, and for each cause they ...
18
votes
9answers
2k views
Missile-mounted cameras
You are employed as Administrator in charge of Road Maintenance and Planning. The intelligence division of the Agency for Road Maintenance and Planning has come up with a brilliant and not at all ...
9
votes
1answer
482 views
Infinite Snake game
Infinite Snake is just like the video game Snake, except for that the snake is infinitely long, there are no items to eat, and the Snake needs to move in a repeating ...
19
votes
46answers
2k views
Generate list of numbers and their negative counterparts
A recent SO question asks for a convenient one-liner to generate a list of numbers and their negative counterparts in Python.
Given two integers \$1≤a≤b\$, generate all the integers \$x\$ such that \$...
16
votes
5answers
665 views
Conway's $1(0),000 challenge
Background
This challenge is about A004001, a.k.a. Hofstadter-Conway $10000 sequence:
$$
a_1 = a_2 = 1, \quad a_n = a_{a_{n-1}} + a_{n-a_{n-1}}
$$
which starts with
...
11
votes
2answers
397 views
Spanning paths in a tournament on n nodes
The goal of this challenge is to extend the On-Line Encyclopedia of Integer Sequences (OEIS) sequence A038375.
Maximal number of spanning paths in tournament on n nodes.
A tournament on \$n\$ ...
13
votes
9answers
429 views
Minimal Rotate-Right-Double numbers in base n
Task
For a given base \$n \ge 3\$, find the smallest positive integer \$m\$, when written in base \$n\$ and rotated right once, equals \$2m\$. The base-\$n\$ representation of \$m\$ cannot have ...
15
votes
14answers
1k views
Generating generating expressions for sequences
(yes, "generating generating" in the title is correct :) )
Context
In middle (?) school we are taught about sequences and, in particular, we are taught about linear sequences where the ...
12
votes
15answers
2k views
Pseudo-deterministic number generator
Task
Write a function/full program that will be able to produce two different sequences of integers in [0, ..., 9]. You will take an input ...
27
votes
26answers
2k views
Measure the lengths of binary patterns
Let's consider the sequence of the binary representation of positive integers (without any leading zero):
...
21
votes
27answers
3k views
20
votes
5answers
509 views
What can you see on a hexagonal spiral?
This code-golf challenge will have you computing OEIS sequence A300154.
Consider a spiral on an infinite hexagonal grid. a(n) is the number of cells in the part of the spiral from 1st to n-th cell ...
26
votes
14answers
2k views
Counting valid Binary Sudoku rows
Background
Binary Sudoku, also known as Takuzu, Binario, and Tic-Tac-Logic, is a puzzle where the objective is to fill a rectangular grid with two symbols (0s and 1s for this challenge) under the ...
18
votes
34answers
2k views
Ones and Twos for days
Inspiring myself on a recent challenge, we ought to compute a sequence that is very close to A160242.
Task
Your task is to generate the sequence \$ \{s_i\}_{i=0}^\infty \$:
...
12
votes
18answers
946 views
Progressing Two's
Given an positive integer n (including 0 if you decide to support it), output all numbers in the generated sequence up to the index ...
19
votes
10answers
3k views
An unknowably odd function
This challenge initially appeared in this challenge as a an extra brain teaser. I am posting it with permission from the original author so that we can have a formal competition.
Your task here ...
27
votes
9answers
814 views
Mad Libs number sequences
My robot for generating Mad Libs-style sequence challenges has gone rogue! To defeat it, I need you to write code that can solve all the challenges it can crank out.
Your input is three selections ...
18
votes
19answers
2k views
Is this a circular step sequence?
Background
We define a circular step sequence of order \$n\$ as follows:
$$
a_1, a_2, \dots, a_n = \text{Permutation of } 1 \dots n \\
b_i = \min ( |a_{i+1} - a_i|, n-|a_{i+1} - a_i| ), 1 \le i < ...
16
votes
5answers
875 views
How many unique one sided polyominos
Context
From Wikipedia:
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge.
one-sided polyominoes are distinct when none is a translation or rotation of ...
16
votes
12answers
2k views
It's all about the sum of the digits
The sequence
Given an integer \$n>0\$, we define \$a(n)\$ as the lowest positive integer such that there exists exactly \$n\$ positive integers smaller than \$a(n)\$ whose sum of digits is equal ...
22
votes
18answers
2k views
Concentric rings on a snub square tiling
This challenge takes place on the snub square tiling.
Start by choosing any triangle, and color it \$c_1\$.
Next, find all tiles which touch this triangle at any vertex, and color them \$c_2\$. Next, ...
19
votes
13answers
1k views
Number of palindrome splits
In this task you will take as input a non-negative integer \$n\$, and output the number of pairs of non-negative integers \$a,b\$ such that both are palindromes*, \$a \leq b\$, and \$a+b = n\$. For ...
22
votes
9answers
1k views
Counts Of Orderings Containing At Most K Of The Kth Class
This challenge is about the number of orderings which contain at most \$n\$ classes and at most \$k\$ of the \$k^{\text{th}}\$ class.
One way to represent such an ordering is as a sequence of ...
29
votes
27answers
8k views
What's my telephone number?
Introduction
The telephone numbers or involution numbers are a sequence of integers that count the ways \$n\$ telephone lines can be connected to each other, where each line can be connected to at ...
