# Generate the hailstone sequence without an index
create or replace function hailstone(start) as table (
  with recursive cte as (
    select start as n
    union all
    select if( n % 2 = 0, n // 2, 3 * n + 1) as n
    from cte
    where n != 1
  ) from cte
);

# The length of the hailstone sequence of nn using count()
create or replace function hailstone_length(nn) as (
  select count() as n from hailstone(nn)
);

# Return a tuple giving the seed and the hailstone sequence length
create or replace function hailstone_max_of_lengths(mx) as (
  select max_by( (n,hailstone_length(n)), hailstone_length(n))
  from range(1,mx+1) _(n)
);

# Table of lengths (e.g. for use with histogram())
create or replace function hailstone_lengths(mx) as table (
  select hailstone_length(n) as length
  from range(1,mx+1) _(n)
);