ARITHMETIC PROGRESSIONS OF b-NIVEN NUMBERS

Abstract

A positive integer is a $b$-Niven number (or $b$-harshad number) if it is a multiple of the sum of the digits of its base-$b$ representation. For each base $b\ge 2$, the maximum length of a sequence of consecutive $b$-Niven numbers is known to be $2b$. We investigate the maximum lengths of arithmetic progressions of $b$-Niven numbers.