Infinite Sets of Related <i>b</i>-wARH Pairs

Abstract

Let b ≥ 2 be a numeration base. A b -weak additive Ramanujan-Hardy (or b -wARH) number N is a non-negative integer for which there exists at least one non-negative integer A , such that the sum of A and the sum of base b digits of N , added to the reversal of the sum, give N . We say that a pair of such numbers are related of degrees d ≥ 0 if their difference is d . We show for all numeration bases an infinity of degrees d for which there exists an infinity of pairs of b -wARH numbers related of degree d .