func fib(n) is cached {
n < 2 ? 1
: (fib(n-1) + fib(n-2))
}
func zeckendorf(n) {
n == 0 && return '0'
var i = 1
++i while (fib(i) <= n)
gather {
while (--i > 0) {
var f = fib(i)
f > n ? (take '0')
: (take '1'; n -= f)
}
}.join
}
for n (0..20) {
printf("%4d: %8s\n", n, zeckendorf(n))
}