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:
“It is only when we are very happy that we can bear to gaze merrily upon the vast and limitless expanse of water, rolling on and on with such persistent, irritating monotony, to the accompaniment of our thoughts, whether grave or gay. When they are gay, the waves echo their gaiety; but when they are sad, then every breaker, as it rolls, seems to bring additional sadness, and to speak to us of hopelessness and of the pettiness of all our joys.”
—Emmuska, Baroness Orczy (1865–1947)
“Even in ordinary speech we call a person unreasonable whose outlook is narrow, who is conscious of one thing only at a time, and who is consequently the prey of his own caprice, whilst we describe a person as reasonable whose outlook is comprehensive, who is capable of looking at more than one side of a question and of grasping a number of details as parts of a whole.”
—G. Dawes Hicks (1862–1941)