Script collection for analyzing the Collatz function

Name Purpose and Functionality Link

Sequence calculator for 3n+1

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers
  • Calculating of 3n+1 sequences with binary (or decimal) input
  • Choice, if only odd numbers are displayed
  • Choice, to hide even numbers
  • Choice, to hide binary numbers
  • Choice, to hide trinary numbers
  • Choice, to display the number to be added (2n+1)
  • Choice, to hide binary information

sequence_3n+1.php

Sequence calculator for 3n+1

Date: 16/03/2025
Version: 1.1

Technology: PHP with GMP for large numbers, prime numbers in database
  • Calculating of 3n+1 sequences with binary (or decimal) input
  • Choice, if only odd numbers are displayed
  • Highlight 2k-1 part of numbers in red
  • Highlight 2k+1 part of numbers in blue
  • Highlight alias part(s) of numbers in green
  • Display of numbers n and what to add in decimal and binary format
  • Display prime factors of n and what to add

sequence_3n+1_m2k.php

Calculator for 3n+1 sequences in up/down format

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers
  • Input of Start and end of sequences to be calculated

sequences_3n+1.php

Development of Reverse of the Collatz function with only odd numbers

Date: 21/01/2025
Version: 1.0

Technology: PHP with TXT-Database
  • Nothing to choose
  • Displays in each step, which numbers are reached with Alias and Precursor

reverse_3n+1.php

Reverse of the Collatz function with only odd numbers

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers
  • Selection of a former number (if possible)

build_3n+1.php

Develpment of Bitwidth of binary numbers

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers
  • Calculates a bar chart with binary (or decimal) input
  • Hover of a bar displays:
    • iteration number
    • value
    • bitwidth
    • amount of selected bits (1) in red
    • unselected bits (0) in blue

bitwidth_OZ_3n+1.php

Develpment of Bitwidth of binary numbers

Date: 21/01/2025
Version: 1.0
Technology: PHP with GMP for large numbers, CanvasJS
  • Calculates a bar chart with binary (or decimal) input
  • Hover of a bar displays:
    • iteration number
    • value
    • bitwidth
    • amount of trits (0) in green
    • amount of trits (1) in red
    • amount of trits (2) in blue

tritwidth_3n+1.php
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Script collection for analyzing the 3n-1 function

Name Purpose and Functionality Link

Sequence calculator for 3n-1

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers
  • Calculating of 3n-1 sequences with binary (or decimal) input
  • Choice, if only odd numbers are displayed
  • Choice, to hide even numbers
  • Choice, to hide binary numbers
  • Choice, to hide trinary numbers
  • Choice, to display the number to be added (2n+1)
  • Choice, to hide binary information

sequence_3n-1.php

Sequence calculator for 3n-1
Date: 17/03/2025
Version: 1.2

Technology: PHP with GMP for large numbers, prime numbers in database
  • Calculating of 3n-1 sequences with binary (or decimal) input
  • Choice, if only odd numbers are displayed
  • Highlight 2k-1 part of numbers in red
  • Highlight 2k+1 part of numbers in blue
  • Highlight alias part(2) of numbers in green
  • Display of numbers n and what to add in decimal and binary format
  • Display prime factors of n and what to add

sequence_3n-1_m2k.php

Calculator for 3n-1 sequences in up/down format

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers
  • Input of Start and end of sequences to be calculated
  • Selection of the Sequence(s)

sequences_3n-1.php

Development of Reverse of the 3n-1 function with only odd numbers

Date: 18/01/2025
Version: 1.0

Technology: PHP with TXT-Database
  • Nothing to choose
  • Displays in each step, which numbers are reached with Alias and Precursor

reverse_3n-1.php

Reverse of the 3n-1 function with only odd numbers

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers
  • Selection of a former number (if possible)

build_3n-1.php

Develpment of Bitwidth of binary numbers of a 3n-1 sequence

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers
  • Calculates a bar chart with binary (or decimal) input
  • Hover of a bar displays:
    • iteration number
    • value
    • bitwidth
    • amount of selected bits (1) in red
    • unselected bits (0) in blue

bitwidth_OZ_3n-1.php

Develpment of Bitwidth of trinary numbers of a 3n-1 sequence

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large numbers, CanvasJS
  • Calculates a bar chart with binary (or decimal) input
  • Hover of a bar displays:
    • iteration number
    • value
    • bitwidth
    • amount of trits (0) in green
    • amount of trits (1) in red
    • amount of trits (2) in blue

tritwidth_3n-1.php
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Sequence calculator for 5n+1

Name Purpose and Functionality Link

Sequence calculator for 5n+1

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large number
  • Calculating of 5n+1 sequences with binary (or decimal) input
  • Choice, if only odd numbers are displayed
  • Choice, to hide even numbers
  • Choice, to hide binary numbers
  • Choice, to hide trinary numbers
  • Choice, to display the number to be added (2n+1)
  • Choice, to hide binary information

sequence_5n+1.php
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Script for Comparing values of 3n+1, 3n-1 and (3n+1)+(3n-1)

Name Purpose and Functionality Link

Comparing of values

Date: 21/01/2025
Version: 1.0

Technology: PHP with GMP for large number
  • Calculating odd Values of 3n+1, 3n-1 and (3n+1)+(3n-1)
  • Choice, to display/hide numbers in binary format
  • Choice, to display/hide results of 3n+1
  • Choice, to display/hide results of 3n-1
  • Choice, to display/hide results of (3n+1)+(3n-1)

compare_3n-1+1.php
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Sources for Prime Numbers (2024)

Name Purpose and Functionality Link

Article on Prime Numbers

Date: 16/12/2024
Version: 1.0

Technology: PHP
  • Article on Prime Numbers (eng, ger, ukr)

English:
article.html
German:
article_de.html
Ukrainian:
article_ua.html

Sine Curves of Prime Numbers

Date: 16/12/2024
Version: 1.0

Technology: PHP CanvasJS
  • Generating Sine Curves for several preselected prime numbers

fin_sine.php

Table of Prime Numbers

Date: 16/12/2024
Version: 1.0

Technology: PHP
  • Marks prime numbers in a table with preselected size

fin_table.php

Development of Prime Numbers

Date: 16/12/2024
Version: 1.0

Technology: PHP
  • Display on the development of prime numbers

fin_rectangles.php

Diagram to analyse natural numbers

Date: 16/12/2024
Version: 1.0

Technology: PHP
  • Diagram to analyse natural numbers (interactive)

fin_diagram_only.php

Development of Prime Numbers

Date: 16/12/2024
Version: 1.0

Technology: PHP
  • Explanation on the development of prime numbers

Interactive:
fin_instruction2.php
Explanation:
fin_instruction.html
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