greedy_egyptian_fractions.sf

#!/usr/bin/ruby

# Greedy algorithm for Egyptian fractions

# See also:
#   https://oeis.org/A001466
#   https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions

func egyptian_denominators(r, count=8) {
    gather {
        count.times {
            r -= 1/take(ceil(1/r))
        }
    }
}

say egyptian_denominators(Num.pi)
say egyptian_denominators(Num.pi).sum { 1/_ }

__END__
[1, 1, 1, 8, 61, 5020, 128541455, 162924332716605980]
3.14159265358979323846264338327950284945450236218