A happy number is 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 equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers).
Read more about Happy Number: Overview, Sequence Behavior, Happy Primes, Special Happy Numbers, Happy Numbers in Other Bases, Cubing The Digits Rather Than Squaring, Origin, Popular Culture, Programming Example
Famous quotes containing the words happy and/or number:
“Montesquieu well knew, and justly admired, the happy constitution of this country [Great Britain], where fixed and known laws equally restrain monarchy from tyranny and liberty from licentiousness.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Again, the great number of cultivated men keep each other up to a high standard. The habit of meeting well-read and knowing men teaches the art of omission and selection.”
—Ralph Waldo Emerson (1803–1882)