# Posts tagged sequence

Challenge A Niven number is a positive integer which is divisible by the sum of its digits. For example, 81 -> 8+1=9 -> 81%9=0. Your task is to find the first n Niven numbers, given n. Te...

Introduction The Pell(no, not Bell) Numbers are a simple, Fibonacci-like sequence, defined by the following relation: $P_n=\begin{cases}0&\mbox{if }n=0;\\1&\mbox{if }n=1;\\2P_{n-1}+P_{n-2...

Inspired by this challenge. If anyone has any suggestions for a song title I could use for the challenge title then please leave a comment. Definition We define f(x) for a given integer as the su...

Introduction What is the Caesar shift cipher (ROT$n$)? It's basically a cipher sequence that changes a letter's value from the number chosen. If we use ROT1 on "games", we get "hbnft". The basic i...

The Ludic Numbers are a sequence that pops up when you apply the sieve of eratosthenes to the natural numbers, completely removing the numbers every iteration. Here is how they are generated: The...

Definition $F_{n}\left(0\right)=0$ $F_{n}\left(1\right)=1$ $F_{n}\left(x\right)=n\cdot F_{n}\left(x-1\right)+F_{n}\left(x-2\right)$ For example: $F_{1}=\left[0,1,1,2,3,5,8,13,21,34,55,89...\ri...

Challenge Create a program that takes input of a string and outputs an integer using the following calculation system: The string can only contain +, -, *, /, ^, ! (or a different character; ! ...

A Juggler sequence is a sequence that begins with a positive integer $a_0$ and each subsequent term is calculated as: $$a_{k+1} = \begin{cases} \left \lfloor a_k ^ \frac 1 2 \right \rfloor, &...

Heavily based on this closed challenge from SE. Description A Sumac sequence starts with two non-zero integers $t_1$ and $t_2.$ The next term, $t_3 = t_1 - t_2$ More generally, $t_n = t_{n-2} ...