Task: Summarize and say sequence







Python: from itertools import groupby, permutations

def A036058(number):
    return ''.join( str(len(list(g))) + k
                    for k,g in groupby(sorted(str(number), reverse=True)) )

def A036058_length(numberstring='0', printit=False):
    iterations, last_three, queue_index = 1, ([None] * 3), 0

    def A036058(number):
        
        return ''.join( str(len(list(g))) + k
                        for k,g in groupby(number) )

    while True:
        if printit:
            print("  %2i %s" % (iterations, numberstring))
        numberstring = ''.join(sorted(numberstring, reverse=True))
        if numberstring in last_three:
            break
        assert iterations < 1000000
        last_three[queue_index], numberstring = numberstring, A036058(numberstring)
        iterations += 1
        queue_index +=1
        queue_index %=3
    return iterations
    
def max_A036058_length( start_range=range(11) ):
    already_done = set()
    max_len = (-1, [])
    for n in start_range:
        sn = str(n)
        sns = tuple(sorted(sn, reverse=True))
        if sns not in already_done:
            already_done.add(sns)
            size = A036058_length(sns)
            if size > max_len[0]:
                max_len = (size, [n])
            elif size == max_len[0]:
                max_len[1].append(n)
    return max_len

lenmax, starts = max_A036058_length( range(1000000) )


allstarts = []
for n in starts:
    allstarts += [int(''.join(x))
                  for x in set(k
                               for k in permutations(str(n), 4)
                               if k[0] != '0')]
allstarts = [x for x in sorted(allstarts) if x < 1000000]

print (  % (lenmax, allstarts)   )

print (  )

for n in starts:
    print()
    A036058_length(str(n), printit=True)





Ada: with Ada.Text_IO; use Ada.Text_IO;
with Ada.Containers.Vectors;
procedure SelfRef is
   subtype Seed is Natural range 0 .. 1_000_000;
   subtype Num is Natural range 0 .. 10;
   type NumList is array (0 .. 10) of Num;
   package IO is new Ada.Text_IO.Integer_IO (Natural);
   package DVect is new Ada.Containers.Vectors (Positive, NumList);

   function Init (innum : Seed) return NumList is
      list : NumList := (others => 0);
      number : Seed := innum;  d : Num;
   begin
      loop
         d := Num (number mod 10);
         list (d) :=  list (d) + 1;
         number := number / 10; exit when number = 0;
      end loop; return list;
   end Init;

   procedure Next (inoutlist : in out NumList) is
      list : NumList := (others => 0);
   begin
      for i in list'Range loop
         if inoutlist (i) /= 0 then
            list (i) := list (i) + 1;
            list (inoutlist (i)) := list (inoutlist (i)) + 1;
         end if;
      end loop; inoutlist := list;
   end Next;

   procedure Show (list : NumList) is begin
      for i in reverse list'Range loop
         if list (i) > 0 then
            IO.Put (list (i), Width => 1); IO.Put (i, Width => 1);
         end if;
      end loop; New_Line;
   end Show;

   function Iterate (theseed : Seed; p : Boolean) return Natural is
      list : NumList := Init (theseed);
      vect : DVect.Vector;
   begin
      vect.Append (list);
      loop
         if p then Show (list); end if;
         Next (list); exit when vect.Contains (list); vect.Append (list);
      end loop;
      return Integer (DVect.Length (vect)) + 1;
   end Iterate;

   mseed : Seed;
   len, maxlen : Natural := 0;
begin
   for i in Seed'Range loop
      len := Iterate (i, False);
      if len > maxlen then mseed := i; maxlen := len; end if;
   end loop;
   IO.Put (maxlen, Width => 1); Put_Line (" Iterations:");
   IO.Put (mseed, Width => 1); New_Line;
   len := Iterate (mseed, True);
end SelfRef;