Questions tagged [sequence]
For challenges involving sequences, typically of numbers following some pattern.
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Sylvester primes
Sylvester's sequence can be defined recursively S(n) = S(n-1)*(S(n-1) + 1) for n >= 1 starting S(0) = 1.
Since S(n) and S(n) + 1 have no common divisors, it follows that S(n) has at least one more ...
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Sums of X*Y chunks of the nonnegative integers
Consider the infinite table of the nonnegative integers with width 12:
...
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Rabinowitz-Wagon \$\pi\$ formula
In 1995, Stanley Rabinowitz and Stan Wagon found an interesting algorithm to generate the digits of \$\pi\$ one by one without storing the previous results. The algorithm is called the spigot ...
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Non-Decreasing Fibonacci Sequence modulo M
Given integers \$a,b,m, k, n\$ and array \$F = (f_1, f_2,...,f_n)\$ defined as:
\begin{cases}
f_1 = \text{a}\\
f_2 = \text{b}\\
f_i = (f_{i-1} + f_{i-2}) \text{ mod m},∀i > 2
\end{cases}
When \$F\$ ...
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Generate a subgroup of a free group
In group theory, the free group with \$n\$ generators can be obtained by taking \$n\$ distinct symbols (let's call them \$a, b, c ...\$ etc), along with their inverses \$ a^{-1},b^{-1},c^{-1} ...\$ . ...
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Smallest Harmonic number greater than N
The sequence of Harmonic numbers are the sums of the reciprocals of the first k natural numbers (not including zero):
\${\displaystyle H_{k}=1+{\frac {1}{2}}+{\frac {1}{3}}+\cdots +{\frac {1}{k}}=\sum ...
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Where are zeros? Self-describing sequence
Background
A167519: Lexicographically earliest increasing sequence which lists the positions of the zero digits in the sequence.
...
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Golfing the complexity with subtraction
The Mahler-Popken complexity, \$C(N)\$, of a positive integer, \$N\$, is the smallest number of ones (\$1\$) that can be used to form \$N\$ in a mathematical expression using only the integer* \$1\$ ...
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*Trivial* near-repdigit perfect powers
Task
Output the sequence that precisely consists of the following integers in increasing order:
the 2nd and higher powers of 10 (\$10^i\$ where \$i \ge 2\$),
the squares of powers of 10 times 2 or 3 (...
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Enumerate all matches of a regex
related
For this challenge, we'll be using a simplified dialect of regular expressions, where:
A lowercase letter from a to z ...
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Output a 1-2-3-5-7... sequence
Follow-up of my previous challenge, inspired by @emanresu A's question, and proven possible by @att (Mathematica solution linked)
For the purposes of this challenge, a 1-2-3-5-7... sequence is an ...
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Output a 1-2-3 sequence
For the purposes of this challenge, a 1-2-3 sequence is an infinite sequence of increasing positive integers such that for any positive integer \$n\$, exactly one of \$n, 2n,\$ and \$3n\$ appears in ...
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Odds for second smallest prime factor
Given a prime number \$p\$ output the asymptotic density of the set of positive integers which have \$p\$ as their second-smallest distinct prime factor
Input/Output
Input: one of the following ...
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Rank poker High Card hands [closed]
In the poker game there are 1277 unique 'High Card' ranks. It's 1287 (13 over 5) if we include all straights.
The challenge is to write a function which returns an integer value corresponding to the ...
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How quickly can you type this unary string?
If I want to type the string aaa, the least keystrokes I can type it in is 3: a a a. But if I want to type the string ...
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Pretty Palintiples
Imagine you have a positive integer number \$n\$. Let \$m\$ be the number obtained by reversing \$n\$'s digits. If \$m\$ is a whole multiple of \$n\$, then \$n\$ is said to be a reverse divisible ...
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Enumerate the Phat-fingered-lights-out numbers
Even though the concept of phat-fingered-lights-out number should be pretty self-explanatory here is a definition:
Given a nonnegative integer in binary representation a phat-fingered double-bit-flip ...
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Alternating Random Series Sum To \$N\$ [closed]
Challenge
Given a positive integer \$N \ge 3\$, generate an alternating series of \$N\$ random numbers within the range \$[1, N]\$, such that their sum equals \$N\$. Expressed mathematically as
$$N = ...
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votes
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Double-reduce a sequence of integers
Consider a function \$r\$ where
$$
r(i,k)= \begin{cases}
L_{i+1}-L_i, & \text{if}\ k =0\ \text{ (1st reduction)} \\
r(i,0)-r(\lfloor \log_2{k} \rfloor,k-2^{\lfloor \log_2{k} \rfloor}) & \text{...
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Binary Expansion Counting Sequence
I found another sequence not yet in the OEIS
The binary expansion sequence is defines as follows, assuming 0 indexing:
The even numbers of the sequence are how often 0 has appeared in the binary ...
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Mousetail's Sequence
I define mousetail's sequence as follows:
If the nth element of the sequence is q, then n+1 must appear q times in the sequence
The sequence is weakly monotonically increasing (i.e. no lower number ...
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Exact Sum of 1/2 to 1/n [duplicate]
Consider the sequence 1/2, 1/3 + 1/2, 1/4 + 1/3 + 1/2, and so on. In mathematical symbols, this is
$$S(n)=\sum_{m=2}^{n+1}\frac{1}{m}$$
where S is the function that makes the sequence.
Outputting this ...
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How many Carlitz compositions are there?
OEIS sequence A003242 comprises the numbers of Carlitz compositions for any given positive integer. This is the number of integer partitions of the integer for which no two adjacent parts are equal.
...
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Output an infinitely proportional sequence
In this challenge, an infinitely proportional sequence is defined as a infinite sequence of positive integers such that:
All positive integers are contained infinitely many times within the sequence.
...
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Test whether a sequence is bitonic
You know what a monotonic sequence is: each element is bigger than its predecessor (monotonically rising) or as its successor (monotonically falling).
Bitonic means you have two arms of the sequence, ...
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Construct the Constructability sequence
Consider compass-and-straightedge construction, where you can construct new points from existing ones by examining intersections of straight lines and circles constructed with one of the following two ...
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Rudin-Shapiro sequence
The Rudin-Shapiro sequence is a sequence of \$1\$s and \$-1\$s defined as follows: \$r_n = (-1)^{u_n}\$, where \$u_n\$ is the number of occurrences of (possibly overlapping) \$11\$ in the binary ...
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Monotone sequence beatitude
Provided that the input is a monotone sequence of three or more integers:
Output -2 if the sequence strictly decreases. Example: [7,4,3,2]
Output -1 if the ...
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Minecraft XP Orb Amounts
In the video game Minecraft, the player can obtain experience points (XP) from various activities. In the game, these are provided as XP "orbs" of various sizes, each of which give the ...
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Divisor chain counts (1 3 3 7 ...)
The divisors of a natural number form a poset under the relation of "a divides b?", \$a | b\$. This challenge is to produce the number, \$C\$, of non-empty chains of such posets for natural ...
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Diagonal Binary Sequence
Challenge:
Given a positive number \$n\$, convert it to binary, and output a sequence where all 1s form a top-left to bottom-right diagonal line, including a ...
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Make a super fair number
An even distribution number is a number such that if you select any of it's digits at random the probability of it being any particular value (e.g. 0 or ...
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The multiples are missing
Given a number \$n\$, you are to compute the sequence of positive numbers where for each number \$a\$, the \$n\$-times multiple \$n\cdot a\$ is missing.
Example
We always start with the sequence of ...
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Complement an infinite list
In this challenge, we define the complement of a list of positive integers as all positive integers not included in that list. For example, the complement of the even numbers ...
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Longest sequence of Egyptian fractions with n as denominator
Background
From Wikipedia: An Egyptian fraction is the sum of distinct unit fractions. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, ...
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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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votes
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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: $$2, 3, 5, 7, 11, 13, 17, 19, ....
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Give the fool's Fibonacci sequence
Recently I asked for tips on improving some code-golf of mine. The code was supposed to output every third value of the Fibonacci sequence starting with 2:
...
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Encrypting Emojis
Problem
You are tasked with creating a program that performs emoji encryption on a given string of emojis. In this encryption scheme, each emoji is replaced by a unique character (from ...
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Output the smallest increasing sequence where each term is coprime to preceding 3 terms
This sequence is defined as
Starts with 1, 2, 3
The next element of the sequence is the first number greater than the previous three that is co-prime with each of the previous 3 elements in the ...
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Magic OEIS formulae (Robbers' thread)
This is the robbers' thread. See the cops' thread here.
In this cops and robbers challenge, the cops will be tasked with writing an algorithm that computes some function of their choice, while the ...
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Magic OEIS formulae (Cops' thread)
This is the cops' thread. See the robbers' thread here.
In this cops and robbers challenge, the cops will be tasked with writing an algorithm that computes some function of their choice, while the ...
- 22.8k
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The all-high powerful numbers
We've had powerful numbers, yes, but what about highly powerful numbers?
Highly powerful numbers
Let \$n\$ be a positive integer in the form
$$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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