Arithmetic dynamics | Base-dependent integer sequences

Happy number

In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because , and . On the other hand, 4 is not a happy number because the sequence starting with and eventually reaches , the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. A number which is not happy is called sad or unhappy. More generally, a -happy number is a natural number in a given number base that eventually reaches 1 when iterated over the perfect digital invariant function for . The origin of happy numbers is not clear. Happy numbers were brought to the attention of (a British author and senior lecturer in pure mathematics at Leeds University) by his daughter, who had learned of them at school. However, they "may have originated in Russia" (:§E34). (Wikipedia).

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MegaFavNumbers: 1.5 Billion

#MegaFavNumbers What’s your Mega Favourite Number?

From playlist MegaFavNumbers

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MegaFavNumbers: RSA-2048

My own choice for a number over 1,000,000 is this 617 digit boy: 251959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807844069182906412495150821892985591491761845028084891200728449926873928072877767359714183472702618963750149718246911650776133798590

From playlist MegaFavNumbers

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Conversion Arcs and 2,916,485,648,612,232,232,816 (MegaFavNumbers)

I'm sorry. The MegaFavNumbers playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo

From playlist MegaFavNumbers

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Tutorial - What is an imaginary number

http://www.freemathvideos.com In this video playlist you will learn everything you need to know with complex and imaginary numbers

From playlist Complex Numbers

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Different Types of Numbers on the number line, lesson 1 #shorts

Watch the full playlist: https://www.youtube.com/watch?v=kcxK3_sROZA&list=PL14bv5vXK2WWuODhGbpPQA0GamV5ohOVb&index=1 Natural Numbers (N), (also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …} Whole Numbers (W). This is the set of na

From playlist Celebrities Teach Math: The Number System

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Happy Numbers? 😀 | #Shorts #YouTubeShorts | Don't Memorise

What are Happy Numbers? Watch this video to learn more... Don’t Memorise brings learning to life through its captivating educational videos. To Know More, visit https://infinitylearn.com/ New videos every week. To stay updated, subscribe to our YouTube channel: http://bit.ly/DontMemorise

From playlist Shorts

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undergraduate machine learning 9: Hidden Markov models - HMM

Hidden Markov models. The slides are available here: http://www.cs.ubc.ca/~nando/340-2012/lectures.php This course was taught in 2012 at UBC by Nando de Freitas

From playlist undergraduate machine learning at UBC 2012

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MegaFavNumbers.MP4

#MegaFavNumbers

From playlist MegaFavNumbers

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A Fun Thing You Can Do With Topological Combinatorics

This video aims at explaining the connection between the Borsuk Ulam Theorem in topology and its connection with the Tucker's Lemma in the conbinatorics branch of math. The content is based on a direct reading program that took place from Feb. 2022 to Sep. 2022 in University of California,

From playlist Summer of Math Exposition 2 videos

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A friendly introduction to Bayes Theorem and Hidden Markov Models

Announcement: New Book by Luis Serrano! Grokking Machine Learning. bit.ly/grokkingML 40% discount code: serranoyt A friendly introduction to Bayes Theorem and Hidden Markov Models, with simple examples. No background knowledge needed, except basic probability. Accompanying notebook: https

From playlist Mathematics videos

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There are a lot more numbers than I thought there were - MegaFavNumbers

A short video detailing my favorite number larger than 1 million! There are so many numbers out there it was hard to choose from, but I’m glad I could participate in the #MegaFavNumbers series

From playlist MegaFavNumbers

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Aprendizaje automatico - Clasificacion y regresion - Nuevo link: www.youtube.com/watch?v=hkOZ2potocA

ANUNCIO: Este video pronto se movera aca: https://www.youtube.com/watch?v=hkOZ2potocA Los videos en español pronto se moverán a este canal: https://www.youtube.com/channel/UCvnzQ7-7MrsC6AVo5LxnQWw Link to a similar video in english: https://www.youtube.com/watch?v=IpGxLWOIZy4 Este video

From playlist Machine learning en espanol

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10 Habits of Happy People - How To Be Happy

In this video we will be learning how to be happy by understanding the habits of happy people. The Habit Harvester Book: http://amzn.to/2vId844 Get a FREE audiobook of your choice: http://amzn.to/2vIhBng Watch all of the videos in this playlist: https://www.youtube.com/watch?v=qlkeWbKm

From playlist Habit Harvester

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Multi-Armed Bandit : Data Science Concepts

Making decisions with limited information!

From playlist Data Science Concepts

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Happy Couple Numbers? #Shorts #YouTubeShorts | Don't Memorise

Everyone dreams of being in a happy relationship or being a happy couple! Do numbers also wish for the same? Check this video out! Don’t Memorise brings learning to life through its captivating educational videos. To Know More, visit https://infinitylearn.com/ New videos every week. To

From playlist Shorts

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Lec 24 | MIT 9.00SC Introduction to Psychology, Spring 2011

Lecture 24: Conclusions - Evolutionary Psychology, Happiness Instructor: John Gabrieli View the complete course: http://ocw.mit.edu/9-00SCS11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 9.00SC Introduction to Psychology, Fall 2011

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145 and the Melancoil - Numberphile

More Matt: http://bit.ly/Matt_Videos Matt Parker talks us through "Happification" and resulting structures it creates. Includes his fascinating Melancoil!? More links & stuff in full description below ↓↓↓ Our earlier Happy Numbers video is at http://www.youtube.com/watch?v=kC6YObu61_w and

From playlist Matt Parker (standupmaths) on Numberphile

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Python Programming 16. Sub Procedures

This is the 16th in a course of computer science video lessons introducing programming with Python. This lesson introduces sub procedures. When you are writing applications, it is good practice to avoid long repetitive programs. Sub programs like sub procedures and functions make this p

From playlist Python Programming Step by Step

Related pages

Fortunate number | Prime number | Iterated function | Natural number | Number theory | Perfect digital invariant | Periodic point | Mersenne prime | Palindromic prime | Pure mathematics | Lucky number | Arithmetic dynamics | Harshad number | Natural density | Cycle detection