a = vector(10 000)	\\ inverse to A109852
small = vector(#a)	\\ small values as (k, A109852(k))
s = 0
unseen = 1
set(n,v) = a[v]=n; small[s++]=[n,v]; while (a[unseen], print (unseen " " a[unseen]); if (unseen++>#a, quit))

{
	for (x=0, oo,
		set(2^x, unseen);
		my (z=s-1);
		forstep (i=z, 1, -1,
			forstep (m=ceil(unseen/small[i][2])*small[i][2], #a, small[i][2],
				if (!a[m],
					my (k=2^x-small[i][1]);
					set(2^x+k, m);
					break;
				);
			);
		);
	);
}

quit