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 }

a(n) = {
	my (r=toruns(n), z=2);
	while (z <= #r,
		if (r[z] > 1,
			r = concat([
				r[1..z-1],
				[1, r[z]-1],
				r[z+1..#r]
			]);
		);
		z += 2;
	);
	fromruns(r);
}

for (n=0, 2^13-1, print (n " " a(n)))

quit