s = 0
unseen = 1
seen(v) = bit test(s, v)
see(v) = s = bit or(s, 2^v); while (seen(unseen), unseen++)

ok(p,v) = {
	my (d=digits(v), t=p%10, w=t%2==0);
	for (k=1, #d,
		if (w && d[k]<=t,
				return (0),
				w=(t=d[k])%2==0
		);
	);
	return (1);
}

other(p) = {
	see(p);
	for (v=unseen, oo,
		if (!seen(v),
			if (!ok(1,v),
					see(v)
			);
			if (!seen(v) && ok(p,v),
				return (v);
			);
		);
	);
}

\\ A377912 Numbers such that every even digit except the last is immediately followed by a strictly larger digit.
is(n) = {
	my (d = digits(n));
	for (i = 1, #d-1,
		if (d[i]%2==0 && d[i] >= d[i+1],
			return (0);
		);
	);
	return (1);
}

b = [0]

c = vector(10 000)
u = 1

{
	for (n = 1, oo,
		v = if (n==1, 0, other(v));	

		if (v > b[#b],
			b = concat(b, select(is, [b[#b]+1..v]));
		);

		w = setsearch(b, v);
		if (w <= #c,
			c[w] = n;
			while (c[u],
				print (u " " c[u]);
				if (u++ > #c,
					break (2);
				);
			);
		);
	)
}

quit