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Questions tagged [sequence]

For challenges involving some sort of sequence.

-3
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1answer
462 views
+50

Output first \$n\$ digits of \$\pi^{1/\pi}\$

This challenge is to produce the shortest code for the constant \$\pi^{1/\pi}\$. Your code must output the first \$n\$ consecutive digits of \$\pi^{1/\pi}\$, where \$n\$ is given in the input. ...
17
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15answers
1k views

Divisor Rich and Poor Numbers

Introduction In the strange world of integer numbers, divisors are like assets and they use to call "rich" the numbers having more divisors than their reversal, while they call "poor" the ones having ...
20
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16answers
3k views

​Cuban​ ​Primes

Given a natural number \$n\$, return the \$n\$-th cuban prime. Cuban Primes A cuban prime is a prime number of the form $$p = \frac{x^3-y^3}{x-y}$$ where \$y>0\$ and \$x = 1+y\$ or \$x = 2+y\$ ...
31
votes
19answers
2k views

Hostile Divisor Numbers

Some divisors of positive integers really hate each other and they don't like to share one or more common digits. Those integers are called Hostile Divisor Numbers (HDN) Examples Number <...
8
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9answers
1k views

Shantae Dance Matching

In the original Shantae game, there are transformation dances that you have to input in time using the D-Pad, A, and B. If you complete a predefined sequence while dancing, you will transform into the ...
13
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10answers
1k views

New Order #6: Easter Egg

Introduction (may be ignored) Putting all positive integers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all ...
26
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12answers
2k views

The Nth Gryphon Number

I came up with a series of numbers the other day and decided to check what the OEIS number for it was. Much to my surprise, the sequence did not appear to be in the OEIS database, so I decided to ...
35
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21answers
3k views

List *all* the tuples!

Write a program, given an input n, will generate all possible n-tuples using natural numbers. ...
16
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5answers
654 views

New Order #5: where Fibonacci and Beatty meet at Wythoff

Introduction (may be ignored) Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all ...
17
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19answers
2k views

New order #4: World

Introduction (may be ignored) Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all ...
44
votes
41answers
10k views

Patience, young “Padovan”

Everyone knows the Fibonacci sequence: You take a square, attach an equal square to it, then repeatedly attach a square whose side length is equal to the largest side length of the resulting rectangle....
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0answers
47 views

Count using letters [duplicate]

What to do? Starting from a, count in the sequence: ...
16
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6answers
332 views

New Order #3: 5 8 6

Introduction (may be ignored) Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all ...
13
votes
3answers
359 views

Counting the number of restricted forests on the Möbius ladder of length n

OEIS sequence A020872 counts the number of restricted forests on the Möbius ladder Mn. The Challenge The challenge is to write a program that takes an integer as an input ...
15
votes
11answers
772 views

New Order #2: Turn My Way

Introduction (may be ignored) Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all ...
12
votes
10answers
578 views

New Order #1: How does this feel?

Introduction Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all positive numbers. ...
14
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11answers
860 views

Source permutation

A permutation of a set \$S = \{s_1, s_2, \dotsc, s_n\}\$ is a bijective function \$\pi: S \to S\$. For example, if \$S = \{1,2,3,4\}\$ then the function \$\pi: x \mapsto 1 + (x + 1 \mod 4)\$ is a ...
25
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28answers
3k views

Make me a metasequence

Background For this challenge, a 'metasequence' will be defined as a sequence of numbers where not only the numbers themselves will increase, but also the increment, and the increment will increase ...
12
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18answers
939 views

Jumping Numbers

A jumping number is defined as a positive number n which all pairs of consecutive decimal digits differ by 1. Also, all single digit numbers are considered jumping numbers. eg. 3, 45676, 212 are ...
9
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10answers
407 views

Generate a Baseball Pitch String

Goal Write a program or function that takes a positive integer n and randomly generate a legal series of pitches (a Pitch string) of length ...
19
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25answers
2k views

The Highest Dice

Challenge: Here we have the first 100 items of a sequence: ...
26
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13answers
2k views

Superpermutations

Introduction You're a criminal tasked with stealing some secret plans from the new tech startup Dejavu. You sneak in over the back wall, but find a door that requires a pin to open it. You recognize ...
23
votes
3answers
1k views

The Path Of The Wildebeest

Golf a program or function which gives the \$n^{\text{th}}\$ location of the wildebeest who starts at square \$1\$ on an infinite chessboard which is numbered in an anti-clockwise square spiral, where ...
16
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4answers
677 views

Number of \$n\$-carbon alkanes

Given a positive number \$n\$, find the number of alkanes with \$n\$ carbon atoms, ignoring stereoisomers; or equivalently, the number of unlabeled trees with \$n\$ nodes, such that every node has ...
16
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23answers
2k views

Find if a list is an ABC-triple

Three positive integers A, B, C are ABC-triple if they are coprime, with A < B and satisfying the relation : A + B = C Examples : 1, 8, 9 is an ABC-triple ...
23
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18answers
2k views

Collapsing numbers

Let's define the a function on natural numbers \$n\$, written as base 10 digits \$d_k\; d_{k-1}\; \dotsc\; d_1\; d_0\$, as follows: As long as there are equal adjacent digits \$d_i\;d_{i-1}\$, ...
28
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2answers
735 views
+500

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 ...
25
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46answers
4k views

Draw some expanding arrows

This challenge is about printing a series of growing ASCII-art arrows. I'll describe the pattern in words, but it might be easier to look at what the start of this series looks like: ...
21
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26answers
2k views

Digital Sumorial

Given an input n, write a program or function that outputs/returns the sum of the digital sums of n for all the bases 1 to ...
13
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20answers
1k views

Number in Number-squared

Consider a sequence of natural numbers for which N appears as a substring in N^2. A018834 Output the nth element of this sequence. Rules Program takes only ...
32
votes
46answers
5k views

Print all lexicographically increasing numbers under 10000

A lexicographically increasing number is an integer whose digits are in strictly increasing order. Print all lexicographically increasing numbers under 10000. Here are lines of the expected output: ...
13
votes
11answers
1k views

Terms of the EKG sequence

Introduction The EKG sequence begins with 1 and 2, then the rule is that the next term is the smallest positive integer not already in the sequence and whose common factor with the last term is ...
9
votes
5answers
201 views

Find the minimal initial values [duplicate]

Consider a sequence F of positive integers where F(n) = F(n-1) + F(n-2) for n >= 2. The ...
24
votes
25answers
1k views

New Neighbour Sequence

The non-negative integers are bored of always having the same two* neighbours, so they decide to mix things up a little. However, they are also lazy and want to stay as close as possible to their ...
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19answers
2k views

The Written Digits Sequence

Here's a reasonably trivial sequence which is not in the Online Encyclopedia of Integer Sequences. Start with an empty sequence then define each term as the number of characters required to write out,...
21
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23answers
2k views

Minimal Power Root

The minimal power iteration of a number \$n\$ is defined as follows: $$\text{MPI}(n):=n^{\text{min}(\text{digits}(n))}$$ That is, \$n\$ raised to the lowest digit in \$n\$. For example, \$\text{MPI}(...
20
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65answers
5k views

Display numbers lacking 2's

Display numbers from one to one-hundred (in increasing order), but number 2 shouldn’t appear anywhere in the sequence. So, for example, the numbers two (2) or ...
16
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21answers
2k views

How many threes?

In this task your code will be given an integer \$n\$ as input. Your code should then output the greatest number of multiples of \$3\$ that can be concatenated (in base \$10\$) to form \$3n\$ (with ...
13
votes
10answers
1k views

Quadratic residues are so much fun!

Definitions Quadratic residues An integer \$r\$ is called a quadratic residue modulo \$n\$ if there exists an integer \$x\$ such that: $$x^2\equiv r \pmod n$$ The set of quadratic residues modulo \...
12
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2answers
276 views

Removing points from a triangular array without losing triangles

I have a combinatorics problem that I'd like to put on the OEIS—the problem is that I don't have enough terms. This code challenge is to help me compute more terms, and the winner will be the user ...
4
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3answers
189 views

Hyperoperation Golfing [duplicate]

Introduction In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n = 0), then ...
33
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41answers
5k views

Half, Half Half, and, Half

Consider the following number sequence: \$ 0, \frac{1}{2}, \frac{1}{4}, \frac{3}{4}, \frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}, \frac{1}{16}, \frac{3}{16}, \frac{5}{16}, \frac{7}{16}, \...
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1answer
155 views

Sorting out redundant text from screen scraper application [closed]

You are writing a screen scraper application monitoring a text-only chat window. Text is added at the bottom of the window. The application takes screenshot of the chat window. If a change has ...
7
votes
20answers
425 views

Find the \$\left(n^2\right)^\text{th }n\$-gonal number

Given a non-negative integer, \$n\$, yield the \$(n^2)^\text{th } n\$-gonal number. Further Detail: The \$x\$-gonal numbers, or polygonal numbers, are also known as the two-dimensional figurate ...
7
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0answers
99 views

How long to cross the bridge? [duplicate]

Introduction There is a group of people that have to cross a rickety bridge that can only support two people at a time. It is a dark and foggy night, but unfortunately, the group only has one lamp. ...
12
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17answers
509 views

Compute the minimum \$a(n)>a(n-1)\$ such that \$a(1)+a(2)+\dots+a(n)\$ is prime (OEIS A051935)

Background Consider the following sequence (A051935 in OEIS): Start with the term \$2\$. Find the lowest integer \$n\$ greater than \$2\$ such that \$2+n\$ is prime. Find the lowest integer \$n'\$ ...
17
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22answers
2k views

Sort by what the digit pairs describe

Given a positive integer, we can form a new number that's described by its digits taken pairwise (with a leading 0 added for numbers with odd number of digits). For eg.: 1234 can be read as one 2, ...
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26answers
1k views

A function to take three integers and return a list of integers and alphabet-letters

Challenge We take three positive integers a, b, and c as input. Using these integers, first ...
11
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4answers
320 views

Ex-Increasing Set Sequence

Background An ex-increasing set sequence of order \$N\$ is defined as a sequence of integer sets \$S_1,S_2,\cdots,S_n\$ which satisfies the following: Each \$S_i\$ is a non-empty subset of \$\{1,2,\...
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7answers
739 views