Questions tagged [sequence]
For challenges involving sequences, typically of numbers following some pattern.
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Numbers with Rotational Symmetry
Given an integer, output a truthy value if it is the same upside-down (rotated 180°) or a falsy value otherwise.
0, 1, and <...
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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 ...
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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 ...
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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 ...
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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 ...
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Smallest number such that concatenation is a square
Challenge
Write a program or function that takes a number \$n\$ and returns the smallest \$k\$ such that concatenation \$n'k\$ is a square. This sequence is described by A071176 on the OEIS.
I/O ...
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Is it a semiprime?
Surprisingly, I don't think we have a code-golf question for determining if a number is semiprime.
A semiprime is a natural number that is the product of two (not necessarily distinct) prime ...
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+100
Straighten my corners... diagonally
We can arrange the positive integers like this:
1_| 2 | 5 | 10
4___3_| 6 | 11
9___8___7_| 12
16 15 14 13
That is, in L-shaped brackets expanding down and right ...
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Invalid Invali Inval
This idea is loosely based upon @TùxCräftîñg's chat message.
Take a look at the below example sequence:
INVALID0, INVALID1, <...
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Enumerate all pure sets
In set theory, a set is an unordered group of unique elements. A pure set is either the empty set \$\{\}\$ or a set containing only pure sets, like \$\{\{\},\{\{\}\}\}\$.
Your challenge is to write a ...
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Concatenatable numbers
Given a list of positive integers such as [69, 420], your challenge is to generate the sequence of numbers that can be formed by concatenating numbers from the ...
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Reconstruct an arithmetic sequence
Given a finite arithmetic sequence of positive integers with some terms removed from the middle, reconstruct the whole sequence.
The task
Consider an arithmetic sequence: a list of positive integers ...
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Divinacci Sequence
Divinacci (OEIS)
Perform the Fibonacci sequence but instead of using:
f(n) = f(n-1)+f(n-2)
Use:
...
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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 ...
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Count alternating permutations
An alternating permutation is a permutation of the first \$ n \$ integers \$ \{ 1 ... n \} \$, such that adjacent pairs of values in the permutation alternate between increasing and decreasing (or ...
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Make an n-Juggler
I've been really interested with sequences that follow the property
\$a(n+1) = a(n - a(n))\$
recently, so here's another question about these sequences. In particular we are concerned with ...
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Parenthifiable Binary Numbers
If you express some positive integer in binary with no leading zeros and replace every 1 with a ( and every ...
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Not so triangular numbers
Let's consider the sequence \$S\$ consisting of one \$1\$ and one \$0\$, followed by two \$1\$'s and two \$0\$'s, and so on:
$$1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,...$$
(This is A118175: Binary ...
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Emanresu numbers
My userid is 100664. In binary this is 11000100100111000.
An interesting property of this number is that it can be created entirely by concatenating strings which ...
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Output the Euler Numbers
Given a non-negative integer \$n ,\$ output the \$n^{\text{th}}\$ Euler number (OEIS A122045).
All odd-indexed Euler numbers are \$0 .\$ The even-indexed Euler numbers can be computed with the ...
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Find the nth Fibonacci number, where n is the mth Fibonacci number
Introduction
If \$\newcommand{\fib}{\operatorname{fib}}\fib(x)\$ calculates the \$x\$th Fibonacci number, write a program that calculates \$\fib(\fib(m))\$ for any integer value of \$m \ge 0\$. (Of ...
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Fibonacci reversed!
Introduction
We all know and love our Fibonacci sequence and have seen a myriad of challenge on it here already. However, we're still lacking a very simple case which this answer is going to provide: ...
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Output the Iccanobif Sequence
Write a program or named function that will output or return the sequence up to the nth integer in the Iccanobif sequence, documented on OEIS as A014258. Note that ...
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Output the Juggler sequence
The Juggler sequence is described as follows. Beginning with an input \$a_1\$, the next term is defined by the recurrence relation
$$a_{k+1} = \begin{cases}
\left\lfloor a_k ^ \frac 1 2 \right\rfloor,\...
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Incremental Ranges!
Your task is to, given two positive integers, \$x\$ and \$n\$, return the first \$x\$ numbers in the incremental ranges sequence.
The incremental range sequence first generates a range from one to \$...
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Maximal Substring Construction
In this challenge, you are passed two things:
A string length, N
A list of strings, L, each with an assigned point value. Any ...
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Output a unique sign sequence
A sign sequence is an infinite sequence consisting entirely of \$1\$ and \$-1\$. These can be constructed a number of ways, for example:
Alternating signs: \$1, -1, 1, -1, ...\$
\$-1\$ for primes, \$...
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Irradiated Polyglots
Design a function or program that, when run normally, outputs the triangular numbers. However, when any single character is deleted, the program/function should not function in the original ...
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Euler's numerus idoneus
Euler's numerus idoneus, or idoneal numbers, are a finite set of numbers whose exact number is unknown, as it depends on whether or not the Generalized Riemann hypothesis holds or not. If it does, ...
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Perfect radicals
Given a positive integer number \$n\$ output its perfect radical.
Definition
A perfect radical \$r\$ of a positive integer \$n\$ is the lowest integer root of \$n\$ of any index \$i\$:
$$r = \sqrt[i]{...
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Palindromic Powers
Powers
We define an important power as a number that can be represented as \$ x^y \$ where \$ x ≥ 2 \$ and \$ y ≥ 2 \$.
Palindrome
We define an ...
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Compute the Digit Difference Sum of a Number
Consider taking some non-negative integer such as 8675309 and computing the absolute values of the differences between all the pairs of neighboring digits.
For \$8675309\$ we get \$|8-6| = 2\$, \$|6-7|...
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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 ...
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Multiply or Divide by n
Here's a simple challenge, so hopefully lots of languages will be able to participate.
Given a positive integer \$n\$, output \$A076039(n)\$ from the OEIS.
That is, start with \$a(1)=1\$. Then for \$n&...
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Infinite Candle Sequence
I have a cake shop that specialises in birthday cakes. The cakes that I sell must have candles placed in a circle. You would probably think I can just divide 360° by the number of candles, but the ...
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Reverse and square
In this challenge you will compute numbers from a curious sequence.
Your input is a single decimal nonnegative integer. Reverse the bits in this integer and then square the number to get the required ...
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The Binary Eyes
A binary eye is an odd set of digits, with all of its digits except the center one set to 1 or 0, and the center one set to the opposite of the others. Thus, there are two binary eyes for a given odd ...
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Sequence of integers not the sum of powers of earlier terms
Starting with 1, output the sequence of integers which cannot be represented as the sum of powers of earlier terms. Each previous term can be used at most once, and the exponents must be non-negative ...
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The Rien Number
The Champernowne constant is a number that is constructed by concatenating the first n numbers, with n tending to infinity. It ...
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Print numbers from 1 to 10
This might be a very simple challenge, but I am surprised it hasn't been done on code-golf yet:
Print all Integers from 1 to 10 inclusive in ascending order to standard output.
Your output format ...
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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 by ...
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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 ...
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Find the Missing Numbers in the Fibonacci Sequence Mod K
Inspired by this Math.SE question.
Background
The Fibonacci Sequence (called F) is the sequence, starting 0, 1 such that each ...
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Catalan Numbers
The Catalan numbers (OEIS) are a sequence of natural numbers often appearing in combinatorics.
The nth Catalan number is the number of Dyck words (balanced strings of parenthesis or brackets such as ...
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The Lehmer-Comtet sequence
The Lehmer-Comtet sequence is a sequence such that a(n) is the nth derivative of f(x) = xx with respect to x as evaluated at x = 1.
Task
Take a non-negative integer as input and output the nth term ...
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Join my exclusive friendly club!
Two or more positive integers are said to be "friendly" if they have the same "abundancy". The abundancy of an positive integer \$n\$ is defined as $$\frac {\sigma(n)} n,$$ where \$...
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Fibonacci-orial
Definition
Fibonacci sequence F(n), on the positive integers, are defined as such:
...
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Infinitely many primes
Since Euclid, we have known that there are infinitely many primes. The argument is by contradiction: If there are only finitely many, let's say \$p_1,p_2,...,p_n\$, then surely \$m:=p_1\cdot p_2\cdot.....
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Print a bunch of uninteresting numbers!
An uninteresting number (which I totally didn't make up only for this challenge) is created like this:
Take a positive integer N
Create a new number O by adding the digits of N at the end of N
...
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