a(n) = {
	if(n == 1, return(3));
	my(num = 10^(n-1)+1, e = exp(1), den = num\e, ulim = 10^n, res = 0, delta = ulim, step);
	if(n%2 == 0,
		den = 11 * (floor((den-1)\11)+1);
		step = 11
	,
		step = 1
	);
	print(den);
	while(!ispal(den), den+=step);
	print(den);
	while(num < ulim,
		est = num/den;
		if(gcd(num, den) == 1,
			cdelta = abs(est - e);
			if(cdelta < delta,
				\\print(num" "den);
				delta = cdelta;
				res = [num, den]
			)
		);
		if(est < e,
			num = nxt(num)
		,
			den = nxt(den)
		);
	);
	res[1] \\ res[2] is the corresponding denominator. Replace res[1] by res to print both
}

ispal(n) = fromdigits(Vecrev(digits(n))) == n

nxt(n)=my(d=digits(n)); i=(#d+1)\2; while(i&&d[i]==9, d[i]=0; d[#d+1-i]=0; i--); if(i, d[i]++; d[#d+1-i]=d[i], d=vector(#d+1); d[1]=d[#d]=1); sum(i=1, #d, 10^(#d-i)*d[i])