Parasitic Numbers at Arbitrary Base

Abstract

A natural number is called an {\lambda}-parasitic number if it is multiplied by integer {\lambda} as the rightmost digit moves to the front. The Full set of these numbers is known in the decimal system. Here, a formula to analytically generate parasitic numbers in any base was derived and demonstrated for the number systems in base t = 3, 4, 5, 8, 10 and 16. It allows to generate parasitic numbers with given numbers of periods. The formula was derived using the definition of parasitic numbers , not their cyclical property.