I wrote this query for Dercuano the other day; it computes the Collatz sequence starting from each of the first 100 integers, running a second Collatz computation twice as fast in parallel to detect any cycles (and of course there are none):
with recursive collatz as
(select 1 as x, 1 as n, 1 as m, 0 as p, 0=1 as exit union
select case when nextx then x + 1 else x end as x,
case when nextx then x + 1
else (case n % 2 when 1 then 3*n + 1
else n / 2 end)
end as n,
case when nextx then x + 1
else (case newm % 2 when 1 then 3*newm + 1
else newm / 2 end)
end as m,
case when nextx then 0 else p+1 end as p,
case when nextx then 0 = 1 else n = newm end as exit
from (select (m = 1 or newm = 1) as nextx, x, n, m, p, newm
from (select x, n, m, p,
case m % 2 when 1 then 3*m + 1 else m / 2 end as newm
from collatz where not exit) a) b
where x < 100)
select * from collatz;
It works in Postgres 9.5.14; I'm interested to hear if it works or doesn't in other SQL implementations.
