10 b There are infinitely many 163-165, 1979. In base 10, the 74 6-happy numbers up to 1296 = 64 are (written in base 10): For , Known as a Fake Number, these funny numbers to call have an assortment of international options. 2 b A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1. Iterating this sum-of-squared-digits map always eventually reaches one of the 10 numbers 0, 1, 4, 16, 20, 37, 42, 58, 89, or 145 (OEIS A039943; -unhappy otherwise. A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits. , {\displaystyle F_{2,b}} :P Made by Sean. https://mathworld.wolfram.com/HappyNumber.html. Our courses : https://practice.geeksforgeeks.org/courses/This video is contributed by Anmol Agarwal. 0 https://www.primepuzzles.net/puzzles/puzz_021.htm. F {\displaystyle b} Let the sum of the squares of the digits of a positive integer be represented These are also the numbers whose 2-recurring 2 is the trivial perfect digital invariant 1, and the only cycle is the eight-number cycle. F Use this online calculator to find happy and sad numbers. 32 => 9 + 4 = 13 13 => 1 + 9 = 10 10 => 1 + 0 = 1 // Reached to a sum "1", so 32 is a happy number. This page is visible to subscribers only. b The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, ... (OEIS A007770). Those numbers for which this process ends in 1 are Happy Numbers, while those that do not end in 1 are unhappy numbers. -happy and prime. b Hints help you try the next step on your own. The numbers of happy numbers less than or equal to 1, , , ... are given If the number reaches 1 at the end of the process, the number is said to be Happy, else, unhappy or sad. {\displaystyle b} """, harvtxt error: no target: CITEREFSloane_"A055629" (, "Sequence A161872 (Smallest unhappy number in base n)", On-Line Encyclopedia of Integer Sequences, "Sequence A035502 (Lower of pair of consecutive happy numbers)", "Sequence A072494 (First of triples of consecutive happy numbers)", "Sequence A055629 (Beginning of first run of at least, "Smallest Examples of Strings of Consecutive Happy Numbers", "Sequence A068571 (Number of happy numbers <= 10^n)", https://en.wikipedia.org/w/index.php?title=Happy_number&oldid=1017534979, Articles containing potentially dated statements from 2010, All articles containing potentially dated statements, Articles with disputed statements from December 2017, Creative Commons Attribution-ShareAlike License, This page was last edited on 13 April 2021, at 09:49. Hao Pan, Consecutive happy numbers, arXiv:math/0607213 [math.NT], 2006. b described in the definition of happy given at the top of this article, repeatedly; after each time, they check for both halt conditions: reaching 1, and repeating a number. Practice online or make a printable study sheet. Covering countries like the United States, Canada, Australia, Hungary and Ireland, this number generates a … start with 1880, 4780, 4870, 7480, 7839, ... (OEIS A072494). On the other hand, 4 is not a happy number because the sequence starting with Schwartzman, S. The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English. 37 b , a number Integers that stabilize at 1 are called "happy numbers" and integers that fall into the loop are called "sad numbers”. ( There are two happy numbers: 1st: The numbers between the sequence of the happy number are also happy. Just like in Slither.io, you grow by eating the scatted glowing dots. , https://www.primepuzzles.net/puzzles/puzz_021.htm, https://www.wschnei.de/digit-related-numbers/happy-numbers.html. For instance, while 19 is a 10-happy prime, 91 = 13 × 7 is not prime (but is still 10-happy). [11], In base 12, there are no 12-happy primes less than 10000, the first 12-happy primes are (the letters X and E represent the decimal numbers 10 and 11 respectively).
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