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)
“If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take us as long to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking. All recollected times undergo, accordingly, what M. Ribot calls foreshortening; and this foreshortening is due to the omission of an enormous number of facts which filled them.”
—William James (1842–1910)