Note concerning an odd Langford sequence (Q1840830)

A Langford sequence of defect \(d\) and length \(m\) is a partition of \(\{a_1,a_2,\dots,a_{2m}\}\) into differences \(d,d+1,\dots,d+m-1\). (For example \(\{(5,3),(4,1),(6,2)\}\) is a \(d=2,m=3\) partition of the set \(\{1,2,\dots,6\}\).) In the present paper the author proves as a main result that the set \(\{1,2,\dots,2N+3\}\setminus \{p\}\) can be partitioned into differences \(1,3,\dots, 2N+1\) when \(N\geq 1\) and \(N\neq 1\); \(p\neq 3.\)