for challenges involving some sort of sequence.

learn more… | top users | synonyms

8
votes
0answers
105 views

Count the trees

A tree is a connected, undirected graph with no cycles. Your task is to count how many distinct trees there are with a given number of vertices. Two trees are considered distinct if they are not ...
37
votes
12answers
4k views

A naturally occurring prime generator

There are quite a large number of prime generating functions. Pretty much all of them are constructed and are based on the sieve of Eratosthenes, the Möbius function or the Wilson's theorem and are ...
31
votes
6answers
1k views

Can you reach this number by doubling and rearranging?

Inspired by this question on Math.SE. Starting with 1 you can repeatedly perform one of the following two operations: Double the number. or Rearrange its digits in any way you want, except that ...
17
votes
6answers
797 views

Rise, sequence, rise

We have a strictly increasing sequence of non-negative integers, like: 12 11 10 Wait! This sequence isn't strictly increasing, is it? Well, the numbers are written in different bases. The least ...
21
votes
2answers
713 views

Row of natural numbers

Definition There is infinite row of concatenated natural numbers (positive integers, starting with 1): 1234567891011121314151617181920212223... Challenge Write program in any language, that ...
9
votes
4answers
663 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). ...
9
votes
3answers
318 views

Knödel numbers - Find Kn

Knödel Numbers The Knödel numbers are a set of sequences. Specifically, the Knödel numbers for a positive integer n are the set of composite numbers m, such that all i < m, coprime to m, satisfy ...
17
votes
9answers
529 views

Modular Fibonacci Cycles [duplicate]

The Fibonacci sequence is a well known and famous sequence, where each successive element is the sum of the previous two. A modular Fibonacci sequence is the same, except that the addition is ...
16
votes
12answers
1k views

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 only the zeroth element in the ...
16
votes
11answers
605 views

Grid crossing sequence

If you take a sheet of graph paper and draw a sloped line that goes m units right and n units up, you cross n-1 horizontal and m-1 vertical gridlines in some sequence. Write code to output that ...
12
votes
4answers
453 views

Find primitive semiperfect numbers

Semiperfect numbers A semiperfect/pseudoperfect number is an integer equal to the sum of a part of or all of its divisors (excluding itself). Numbers which are equal to the sum of all of their ...
54
votes
23answers
11k views

xkcd-Style Page Numbering

Randall Munroe's book "xkcd, volume 0" uses a rather odd number system for the page numbers. The first few page numbers are 1, 2, 10, 11, 12, 20, 100, 101, 102, 110, 111, 112, 120, 200, 1000, 1001, ...
10
votes
1answer
440 views

Non-Palindromic Polyglot Boggle

Introduction The number 101 is a palindrome, since it reads the same backwards and forwards. The number 105 is not. However, 105 in base eight is written as 151, which is palindromic. On the other ...
19
votes
9answers
843 views

Calculating Collatz Cousins

Define the function f(n) for a positive integer n as follows: n / 2, if n is even 3 * n + 1, if n is odd If you repeatedly apply this function to any n greater than 0, the result always seems to ...
43
votes
12answers
3k views

Fissile Numbers

I found this sequence while working on Evolution of OEIS, but never got around to posting it as an answer. After writing a reference implementation in Mathematica, I thought this is a fun exercise to ...
13
votes
5answers
355 views

Permutations of the Fifteen Puzzle

The Challenge Consider the following diagram of the Fifteen Puzzle in its solved state: _____________________ | | | | | | 1 | 2 | 3 | 4 | |____|____|____|____| | | | | | ...
13
votes
9answers
925 views

Split as number, join as string, repeat

Consider the process of: Taking a non-negative integer N. e.g. 27. Spliting it into integers N - floor(N/2) and floor(N/2) (a 'bigger' and 'smaller' half) and writing them in that order. e.g.27 ...
7
votes
3answers
228 views

Number of ways to sum [1..n] with [n+1..2n] such that each sum is prime

Let n > 0. Let X = [1..n] and Y = [n+1 .. 2n]. Define a(n) as the number of permutations p of Y such that every element of X + p(Y) is prime. For example: n = 2 X = [1,2] Y = [3,4] p0(Y) = [3,4] ...
11
votes
4answers
585 views

Magic Sequences of length n

A magic sequence is a sequence of non-negative integers x[0..n-1] such that there are exactly x[i] instances of i For instance, 6,2,1,0,0,0,1,0,0,0 is a magic sequence since there are 6 0's, 2 1’s, ...
23
votes
11answers
1k views

Generate Keyboard Friendly Numbers

Most common computer keyboard layouts have the decimal digit keys 1234567890 running along at their top, above the keys for letters. Let a decimal digit's neighborhood be the set of digits from ...
22
votes
35answers
2k views

List all times in the day at a half hour rate

Shortest answer wins. It must be sorted, and in 24hr time. The final line does not have a comma. Output should be as follows: '00:00', '00:30', '01:00', '01:30', '02:00', '02:30', '03:00', '03:30', ...
22
votes
17answers
2k views

Evaluating Dotty Strings

Write a program that takes in an odd length string containing only the characters . and :. With the aid of an initially empty stack, generate a number from this string as follows: For every character ...
43
votes
125answers
4k views

Evolution of OEIS

In this challenge, the goal is to recreate the On-Line Encyclopedia of Integer Sequences one sequence at a time. Similar to the Evolution of Hello World, each answer depends on a previous answer. ...
15
votes
7answers
930 views

Binary Images of Triangle Counts

My challenges tend to be a little bit hard and unattractive. So here something easy and fun. Alcuin's sequence Alcuin's sequence A(n) is defined by counting triangles. A(n) is the number of ...
12
votes
2answers
590 views

Smoothing out a list

You should write a program or function which takes a non-negative integer k and a sorted integer list Las input and outputs or returns a smoothed list M. M is created from the ascending list L by ...
21
votes
4answers
504 views

Reaching one's lucky numbers in reputation

A new code-golfer, Joe, just registered to the site. He has 1 reputation but determined to reach all his lucky numbers in reputation exactly. Joe believes in higher powers which will help him to ...
8
votes
4answers
292 views

Collatz sequence on a two counter machine

The Collatz sequence starting from a positive integer n is defined in this way: if n is even then divide it by 2 (n' = n / 2) if n is odd then multiply it by 3 and add 1 (n' = 3n + 1) Repeat the ...
10
votes
9answers
1k views

Generate The SUDSI Sequence

The SUDSI sequence (sum, difference, swap, increment) is a curious integer sequence that appears to exhibit rather chaotic behavior. It can be generated as follows: Let S be an infinite list of the ...
6
votes
3answers
552 views

Finding Collatz-like rules with many loops

This code-challenge is related to the code-golf question Analyzing Collatz-like sequences but the goal is quite different here. If you are familiar with Collatz-like sequences you can skip to the ...
7
votes
6answers
667 views

Writing code for three tasks

When you run your program first, it should print an integer sequence. The second run should print the 'Mary had a little lamb' song. The third run should produce an ASCII image file. Scoring Your ...
37
votes
18answers
4k views

Shotgun Numbers

The Shotgun numbers are a sequence with a rather simple definition but some interesting structure. Start with the natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ...
13
votes
1answer
198 views

Analyzing Collatz-like sequences

We define a Collatz-like sequence s with 4 positive integers: n starting value d > 1 divisor m > 1 multiplier i increment (In the original Collatz sequence d = 2 m = 3 and i = 1.) Given ...
14
votes
16answers
2k views

Different Way Forward

Given a list of integers produce a Forward Difference at a specified order/depth. For the list of integers: (10, 18, -12, 4, 8, -3, -5, 67, 9, 14) The Forward Differences at the various ...
10
votes
1answer
232 views

Generate a Davenport-Schinzel Sequence

Background A Davenport-Schinzel sequence has two positive integer parameters d and n. We will denote the set of all Davenport-Schinzel sequences for given parameters by DS(d,n). Consider all ...
19
votes
18answers
4k views

Generate Lucky Numbers

Story: Lucy asked George what his Lucky Number was. After some contemplation, George replied that he had several Lucky Numbers. After some brief confusion, Lucy asked George what his first n Lucky ...
9
votes
8answers
545 views

Pair-golfing Twin primes and the Collatz sequence

This is a new kind of challenge inspired by the Recover the mutated source code problem. You should write two programs or functions both in the same language. The first one should solve Task #1 and ...
10
votes
22answers
2k views

Generate the Stöhr sequence

I am learning Ruby and wrote my first nontrivial code to solve this problem. The challenge is to generate the first n elements of the Stöhr sequence, S, which is defined as follows: S[0] = 1 ...
6
votes
6answers
407 views

Mobius inversion

Your goal is to implement Möbius inversion, a linear operation on a sequence of numbers that is used in combinatorics and number theory. Fewest bytes wins. What is Möbius inversion? Given a (finite) ...
9
votes
3answers
447 views

Print the intersection of sequences

Sequences You are given four number sequences, numbered 1 through 4. OEIS The location of 0's when the natural numbers are listed in binary. Here's an example of how to calculate the sequence: ...
7
votes
2answers
340 views

Calculate a pi-based sequence with a pi-based frequence

Introduction Pi is 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089... Let's treat each digit as an instruction as to how to get to the next digit. The first ...
12
votes
11answers
1k views

Make a one sequence

A sequence of integers is a one-sequence if the difference between any two consecutive numbers in this sequence is -1 or 1 and its first element is 0. More precisely: a1, a2, ..., an is a ...
7
votes
4answers
428 views

Generate Eban Numbers

(Continuing on the number sequences code-golf, here is an interesting sequence) Eban Numbers (A006933) are the sequence of numbers whose names (in English) do not contain the letter "e" (i.e., "e" is ...
7
votes
16answers
1k views

Generate Recamán's sequence

Recamán's sequence (A005132) is a mathematical sequence, defined as such: A(0) = 0 A(n) = A(n-1) - n if A(n-1) - n > 0 and is new, else A(n) = A(n-1) + n A pretty LaTex version of the above ...
14
votes
8answers
1k views

Generate Hofstadter's Figure-Figure Sequence

In Gödel, Escher, Bach, Douglas Hofstadter introduces an integer sequence which is commonly referred to as the figure-figure sequence: 2, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, ...
14
votes
15answers
2k views

Generate Ulam Numbers

Given an integer n (where n < 10001) as input, write a program that will output the first n Ulam numbers. An Ulam number is defined as follows: U1 = 1, U2 = 2. For n > 2, Un is the smallest ...
30
votes
31answers
4k views

Lockers vs. Crackers: The Five-Element Sequence

The Challenge A simple "spy versus spy" challenge. Write a program with the following specifications: The program may be written in any language but must not exceed 512 characters (as represented ...
0
votes
1answer
214 views

Write a “Look-and-Say Numbers” generator [duplicate]

There is a sequence of numbers called the "Look-and-Say Numbers". Here is an example of the first 5 terms of the sequence, starting at 1 (with spaces added between the digits): 1 1 1 2 ...
6
votes
5answers
557 views

Output nth term in Catalan type sequence

Given a number, starting with 1, create new numbers (children) by taking the last digit, n, and concatenating 1 through n+1. This seems to be a much better explanation of the sequence A071159. ...
12
votes
5answers
609 views

Stack the deck!

Alice and Bob like to play a card game, with a deck of cards numbered with consecutive nonnegative integers. Alice has a very particular way of shuffling the deck, though. First, she takes the top ...
4
votes
3answers
289 views

Pack sequences of non-negative integers

Let N be the set of nonnegative integers, i.e. {0, 1, 2, 3, ...}. Let c0(N) be the set of all infinite sequences in N that converge to 0, i.e. { (xn) ∈ NN | xn → 0 as n → ∞}. ...