toruns(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); r }
fromruns(r) = { my (v=0); for (k=1, #r, v=(v+k%2)*2^r[k]-k%2); v }

inv(n) = {
	my (r=toruns(n), s=vector(#r));
	for (k=1, #r,
		s[r[k]]=k;
	);
	fromruns(s);
}

{
	vv=[0];
	nb=0;
	for (w=1, 7,
		forperm (w, p,
			if (#vv<nb++,
				vv=concat(vv, vector(#vv));
			);
			vv[nb]=fromruns(p);
		);
	);
	vv=Set(vv[1..nb]);
	for (n=1, #vv,
		print (n " " setsearch(vv, inv(vv[n])));
	);
}

quit