ON THE SUM OF EACH DIGIT'S SQUARE OF INTEGER
Ke Shi · Journal of Qufu Normal University · 1999
The sequence of non_negative integers 4,16,37,58,59,145,42,20, satisfy that the sum of each digit's square of the front one is equal to the next one, the sum of each digit's square of the last one is equal to the first one. For every natural number n , let A (n) 1 denote the sum of each digit;s square of n , and let A (n) k denote the sum of each digit's square of A (n) k-1 , …, So A (n) k form a sequence. Then there exists an integer k 0 , such that as k≥k 0, A (n) k=1 or A (n) k is equal to one of the sequence 4,16,37,58,89,145,42,20.