Questions tagged [sequence]
For challenges involving sequences, typically of numbers following some pattern.
819
questions
27
votes
31answers
3k views
Deranged !Combinatorics: Compute the Subfactorial
The subfactorial or rencontres numbers (A000166) are a sequence of numbers similar to the factorial numbers which show up in the combinatorics of permutations. In particular the nth subfactorial !n ...
36
votes
34answers
2k views
Ken Iverson’s Favourite APL Expression?
Ken Iverson, 1920–2020
Let's implement his favourite expression:
Given a row of Pascal's triangle, compute the next row.
This can for example be computed by taking the input padded with a zero on the ...
29
votes
3answers
1k views
Placing circles along a square spiral
In this code golf challenge, you'll be computing the placement of 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 two ...
14
votes
13answers
916 views
Number of complete rhyme schemes
A rhyme scheme is the pattern of rhymes at the end of the lines in a poem. They are typically represented using letters, like ABAB. We consider two rhyme schemes ...
41
votes
44answers
5k views
The Rien Number
The Champernowne constant is a number that is constructed by concatenating the first n numbers, with n tending to infinity. It ...
27
votes
33answers
5k views
+100
Numbers divisible by the sum and product of their digits
Take a positive integer X. This number is part of the sequence we are interested in if the sum of all digits of X is a divisor ...
19
votes
10answers
1k views
Output every sublist ... eventually
You will be given as input an infinite stream of positive integers.
Your task is to write a program which outputs an infinite sequence of lists with two requirements:
All lists in the output are ...
3
votes
9answers
668 views
Generate Fmbalbuena Numbers
My user id is 106959
How to check if the number is Fmbalbuena number?
First Step: Check if the number of digits is a multiple of 3: ...
9
votes
1answer
328 views
Universal Command Sequence
Universal Command Sequence
Definition
An \$n\$-maze is a \$n\times n\$ chessboard which has "walls" on some edges, and a "king" on the board that can move to the 4 adjacent cells, ...
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 \$...
18
votes
16answers
1k views
Slater-Velez permutation
Let's build a sequence of positive integers. The rule will be that the next number will be the smallest number which:
It hasn't already appeared in the sequence
Its absolute difference from the ...
-6
votes
4answers
114 views
21
votes
24answers
2k views
Next Greater Number
The task:
Given an integer n, find the next number that follows the following requirements
The next greater number is a number where each digit, from left to right,...
106
votes
369answers
18k views
One OEIS after another
As of 13/03/2018 16:45 UTC, the winner is answer #345, by Khuldraeseth na'Barya. This means the contest is officially over, but feel free to continue posting answers, just so long as they follow the ...
16
votes
6answers
729 views
Mutually recursive lists
Let's define a simple function \$f\$ which takes an integer and produces a list:
\$
f(n) = [g(1),g(2),\dots,g(n)] \\
g(n) = [f(0),f(1),\dots,f(n-1)]
\$
We can then calculate the first couple of values ...
136
votes
284answers
35k views
Fibonacci function or sequence
The Fibonacci sequence is a sequence of numbers, where every number in the sequence is the sum of the two numbers preceding it. The first two numbers in the sequence are both 1. Here are the first ...
27
votes
20answers
2k views
13
votes
16answers
861 views
Alternested numbers
Consider the array of positive integers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...
Then, concatenate them:
...
16
votes
27answers
1k views
Output a unique sign sequence
A sign sequence is an infinite sequence consisting entirely of \$1\$ and \$-1\$. These can be constructed a number of ways, for example:
Alternating signs: \$1, -1, 1, -1, ...\$
\$-1\$ for primes, \$...
23
votes
53answers
3k views
Find the sum of the divisors of N
Write a program that displays on the screen the sum of the divisors of a number (1 ≤ N ≤ 100) entered by the user in the range of 1 to N.
This is OEIS A000203.
Examples:
Input: 7
...
33
votes
0answers
948 views
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 [...] ...
15
votes
1answer
378 views
Counting universal n-ary logic gates
Background
A classical logic gate is an idealized electronic device implementing a Boolean function, i.e. one that takes a certain number of Boolean inputs and outputs a Boolean. We only consider two-...
45
votes
54answers
3k views
Output integers in negative order, increase the maximum integer everytime
Main task
Your task is to print out integers in descending order, starting from 1, and increasing as you keep hitting 1 again, up until the given input is reached, then, print out the rest until you ...
34
votes
51answers
5k views
The first n numbers without consecutive equal binary digits
The sequence contains the decimal representation of the binary numbers of the form: 10101..., where the n-th term has n bits.
The sequence is probably easiest to ...
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 ...
25
votes
12answers
5k views
Hamming numbers
Given a positive integer, print that many Hamming numbers, in order.
Rules:
Input will be a positive integer \$n \le 1,000,000 \$
Output should be the first \$n\$ terms of https://oeis.org/A051037
...
25
votes
25answers
2k views
Converge to a number
Your challenge is to, given a positive integer n, count up to each digit of it, giving the effect of converging on it.
Basically, count up to the first digit of n by its place value (\$⌊\log_{10}\left(...
15
votes
18answers
2k views
Prime Factoral Roots
Inspired by digital roots, the prime factoral root of a number is the number that emerges when you take the prime factors of a number, add them together, and repeat the process on the resulting number,...
15
votes
20answers
1k views
Create a pointer sequence
Lets define a pointer sequence to be any sequence such that a(n) = a((n-1)-(a(n-1))) forall n greater than some finite number. For example if our sequence begun with
...
24
votes
31answers
2k views
12
votes
4answers
368 views
The Most Wanted Prime Numbers
Output a sequence of all the primes that are of the following form:
123...91011...(n-1)n(n-1)..11109...321. That is, ascending decimal numbers up to some ...
10
votes
7answers
207 views
Multiplicity of Shared Totients
Euler's totient function, \$\varphi(n)\$, counts the number of integers \$1 \le k \le n\$ such that \$\gcd(k, n) = 1\$. For example, \$\varphi(9) = 6\$ as \$1,2,4,5,7,8\$ are all coprime to \$9\$. ...
10
votes
9answers
518 views
AoCG2021 Day 17: Langton's Hexa-Virus
The story continues from AoC2017 Day 22, Part 2.
The damn virus that was infecting a grid computing cluster now has jumped to a hexagonal computing cluster! In this cluster, the computers are ...
24
votes
12answers
975 views
Nth FizzBuzz Number
Introduction
Everyone knows the FizzBuzz sequence. It goes something like this:
1
2
Fizz
4
Buzz
Fizz
7
8
Fizz
Buzz
11
Fizz
13
14
FizzBuzz
.
.
.
In case you don't ...
13
votes
9answers
2k views
All distances different on a chessboard
Inspired by this Puzzling SE question: All distances different on a chess board.
Introduction
Lets define a sequence \$a(n), n\geqslant 1\$ as how many pawns can you put on a \$n \times n\$ chessboard ...
14
votes
15answers
950 views
Fully matched numbers
For the context of this challenge, a matched group is a digit \$n\$, followed by \$n\$ more matched groups. In the case of \$n = 0\$, that's the whole matched group. Digits only go up to 9.
For ...
26
votes
10answers
2k views
Sum powers to n
Each natural number (including 0) can be written as a sum of distinct powers of integers (with a minimum exponent of 2). Your task is to output the smallest power required to represent \$n\$.
For ...
44
votes
64answers
6k views
An abundance of integers!
An Abundant number is any number where the sum of its proper divisors is greater than the original number. For example, the proper divisors of 12 are:
...
27
votes
40answers
4k views
The plus-minus sequence
The plus-minus sequence
The plus-minus sequence is one that starts with two seeds, a(0) and b(0). Each iteration of this ...
15
votes
19answers
2k views
Harmonic divisor numbers
Consider the \$4\$ divisors of \$6\$: \$1, 2, 3, 6\$. We can calculate the harmonic mean of these numbers as
$$\frac 4 {\frac 1 1 + \frac 1 2 + \frac 1 3 + \frac 1 6} = \frac 4 {\frac {12} 6} = \frac ...
31
votes
2answers
987 views
A spiral sequence
Background
OEIS sequence A272573 describes a spiral on a hexagonal grid as follows:
Start a spiral of numbers on a hexagonal tiling, with the initial hexagon as a(1) = 1. a(n) is the smallest ...
17
votes
23answers
1k views
AoCG2021 Day 3: Say-Look-Say
Part of Advent of Code Golf 2021 event. See the linked meta post for details.
Related to AoC2015 Day 10.
Here's why I'm posting and not Bubbler
The Elves are playing a variation of the game called ...
7
votes
2answers
3k views
Quickly find length of n-th term of the look-and-say sequence
The look and say sequence is an example of a run length encoding sequence. To get the next term of the sequence one groups the sequence into runs of the same number, each group in the next term then ...
18
votes
21answers
987 views
Binomial transform
Background
Binomial transform is a transform on a finite or infinite integer sequence, which yields another integer sequence. The binomial transform of a sequence \$\{a_n\}\$ is given by
$$s_n = \sum_{...
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}|\$ ...
10
votes
13answers
702 views
'Plane' the numbers in any base!
Inspired by this Numberphile video.
What is planing?
In order to 'plane' a sequence of digits, you need to:
Identify the lengths of the 'runs' (adjacently repeated digits) in the sequence. Non-...
15
votes
16answers
2k views
Exponentiation Sequence
The oldest Polish salt mine, located in Bochnia*, was started in year 1248, which we can consider a magical number. We can see that it's equal to 4 digits from the sequence of exponentiations: .
As ...
16
votes
13answers
4k views
Worst case of Slowsort
Background
Slowsort is an in-place, stable sorting algorithm that has worse-than-polynomial time complexity. The pseudocode for Slowsort looks like this:
...
15
votes
6answers
1k views
The Untouchables
Untouchable Numbersα
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself).
...
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46k9 gold badges95 silver badges311 bronze badges
1
vote
2answers
103 views
When the result will reach the people? [closed]
Assume the result of an exam has been published.
After 5 minutes, First person knows the result.
In next 5 minutes, new 8 persons know the result, and in total 9 know it.
Again after 5 minutes, new 27 ...
