Preparation

Preparation

Paradigm(s)	String-rewriting
Designed by	User:Hakerh400
Appeared in	2023
Computational class	Unknown
Major implementations	Implemented
File extension(s)	.txt

Preparation is an esolang invented by User:Hakerh400 in 2023.

Syntax

Source code consists of a single natural number.

Overview

Let $z$ be the natural number from the source code. We define infinite sequence $a_{i}$ such that $a_{0}=z$ and $a_{i+1}=k_{i}\left(k_{i}^{2}-a_{i}\right)$ for any natural number $i$, where $k_{i}=\left\lceil {\sqrt {a_{i}+1}}\right\rceil$. Notation $\left\lceil x\right\rceil$ represents the ceiling function.

Input/Output

There is no input. The output is the sequence $a_{i}$ up to the first repeating number.

Example

Let the source code be $1234$. Here is the sequence $a_{i}$:

1234
2232
3456
1475
1794
2365
1764
3655
4026
4480
603
550
624
25
66
135
108
143
12
16
45
28 <--\
48    |
7     |
6     |
9     |
28 ---/

Explanation. Start with $1234$. Calculate $k_{0}=\left\lceil {\sqrt {1234+1}}\right\rceil =36$ and $a_{1}=36\cdot (36^{2}-1234)=2232$. Continue similarly for the rest of the sequence.

Computational class

The author conjectures that this language is total.

Implementation

Implementation