require "bignum"

local sylvester = {bigint.two}
mpz.init() -- use GMP
mpq.init()
local a = mpz.set(1, 2)
local count = 1
while true do
    local next = mpz.get(a) + 1
    sylvester:insert(next)
    count += 1
    if count == 10 then break end
    mpz.mul(a, next)
end
mpz.clear(a)
print("The first 10 terms in the Sylvester sequence are:")
print(sylvester:mapped(|e| -> e:tostring()):concat("\n"))

a = mpq.set(a, 0)
for sylvester as s do mpq.add(a, bigrat.recip(s)) end
local sum_recip = mpq.get(a)
mpq.clear(a)
print("\nThe sum of their reciprocals as a rational number is:")
print(sum_recip)
print("\nThe sum of their reciprocals as a decimal number (to 211 places) is:")
print(sum_recip:todecimal(211))