ABSTRACT
The number 142,857 has long been recognized by those interested in number oddities as one of the most remarkable of integers. When multiplied by any number from 1 to 6 the result always consists of the same digits and, more remarkably still, these digits always appear in the same cyclic order, but with each number commencing at a different point. Because of this rather striking property 142,857 is called a cyclic number, and it is interesting to proceed further to multiply it by 7, recognizing that there just are no more cyclic combinations of the six digits left to appear. The cyclic numbers have many other surprising and intriguing properties and we shall now touch upon a few more of them. One we have already noticed in connection with the first cyclic number 142,857; it is that when multiplied by its ‘generating prime’ it just produces a lengthy string of nines.
