On Integer Sequences Associated To Two Distinct Sums

Abstract

In this note, we show the existence of integer sequences of lengths at least 3 (except 7) such that for every integer in position $i\equiv 1(\mathrm{mod}4)$ (respectively position $j\equiv 3(\mathrm{mod}4)$), counting from left to right, the sum of the integer and the adjacent integer(s) has a constant sum $x$ (respectively $y$) with $x\ne y$.