Presumably A068340(n)=0 only for n=10; so I looked for n's such that A068340(n)=+/-s; here s=1 (and n<=800000). For s=6, there's no solution at all! For s=8, n=34 (only 1 solution); for s=7, n={55, 56} (2 solutions); for s=9, n={5, 51, 52} (3 solutions) (for n up to 800000).