TITLE:
Infinite Sets of Related b-wARH Pairs
AUTHORS:
Catalin Nitica, Viorel Nitica
KEYWORDS:
Palindrome, Integer Number Theory, Numeration Base
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.10 No.1,
November
11,
2019
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.