Collatz

This small library helps to calculate Collatz sequences with nodejs. Using the big-integer nodejs library this computations can be donde for arbitrary large numbers (examples see below).

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Table of Contents

• Quickstart
• Mathematical Background
• Usage
  • init()
  • number(n)
  • number()
  • toString()
  • length()
  • stoppingTime()
  • sequence()
  • lengths(m,s)
  • stoppingTimes(m,s)
  • iterNumber()
  • isOne()
• Dependencies
• License

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Quick start

Installation

git clone https://github.com/osick/Collatz
cd Collatz
npm install

Run the sample script

cd examples
nodejs example.js

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Mathematical Background

Collatz sequences n_k are defined for k>=0 as follows:

1. Choose an initial number n₀>1
2. For k>=0

• if n_k is even then n_k+1=n_k/2
• else n_k+1=3*n_k+1

For example choose n₀ = 7 then

n₁ = 22
n₂ = 11
...
n₁₄ = 8
n₁₅ = 4
n₁₆ = 2
n₁₇ = 1
n₁₈ = 4
n₁₉ = 2
n₂₀ = 1
n₁₂ = 4 ...

The Collatz Conjecture now is that for any initial number n₀ there is a k>0 s.t. n_k = 1. This conjecture is still open for more than 60 years. For more information see the Wikipedia on Collatz Conjecture .

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Usage

init()

var Collatz = require('collatz.js').Collatz;  

// integer input is supported
var collatz = new Collatz(17);
collatz.init();

// big-integer is supported
var collatz_2 = new Collatz(bigInt(2).pow(5000).add(1));
collatz_2.init();

// strings of digits are supported, e.g.
var collatz_3 = new Collatz("612736124162374123874373678123461782346187293461782347823645");
collatz_3.init();

number(n)

Set the initial number

var collatz = new Collatz("17");
collatz.number("12");
// 12 is the initial number

number()

Returns the initial number

var collatz = new Collatz("17");
collatz.number("12");
console.log(collatz.number());
// Output "12"

toString()

Returns the initial number, synonymous to number()

var collatz = new Collatz("17");
console.log(collatz.toString());
// Output string "17"

length()

Return the length of the Collatz sequence until reaching 1

collatz.number("17");
console.log(collatz.length());
//Output 12

stoppingTime()

Return the stopping time

collatz.number("17");
console.log(collatz.stoppingTime()); 
//Output 3

sequence()

Return the Collatz sequence starting from the initial value

collatz.number("17");
var seq=collatz.sequence();
console.log(seq.toString());
//returns [52,26,13,40,20,10,5,16,8,4,2,1,52,26,13,40,20,10,5,16,8,4,2,1,52,26,13,40,20,10,5,16,8,4,2,1]

iterate()

Iterator to set the class to the next Collatz number in the sequence

collatz.number("17");
console.log(collatz.iterate().toString());
//prints "52"

isOne()

Checks if the current value is "1"

collatz.number("17");
while(!collatz.isOne()){
	console.log(collatz.iterate().toString()+", ");
} 
//prints out "52, 26, 13, ...., 1"

lengths(m,s)

Return an array of lengths m starting from the initial and with stepsize s

collatz.number("17");
console.log(collatz.lengths(20,1).toString());
//Output string "0,20,7,7,15,15,10,23,10,111,18,18,18,106,5,26,13,13,21,21"

stoppingTimes(m,s)

Return an array of stopping times m starting from the initial and with stepsize s

collatz.number("17");
console.log(collatz.stoppingTimes(30,2).toString()); 
//Output string "6,3,8,3,96,3,91,3,6,3,13,3,8,3,88"

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Dependencies

• big-integer NodeJS module

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License

• MIT