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Look-and-say sequence

Look-and-say sequence
You are encouraged to solve this taskaccording to the task description, using any language you may know.

The Look and say sequence is a recursively defined sequence of numbers studied most notably by John Conway.

Sequence Definition

• Take a decimal number
• Look at the number, visually grouping consecutive runs of the same digit.
• Say the number, from left to right, group by group; as how many of that digit there are - followed by the digit grouped.

This becomes the next number of the sequence.

An example:

• Starting with the number 1, you have one 1 which produces 11.
• Starting with 11, you have two 1's i.e. 21
• Starting with 21, you have one 2, then one 1 i.e. (12)(11) which becomes 1211
• Starting with 1211 you have one 1, one 2, then two 1's i.e. (11)(12)(21) which becomes 111221

Task description

Write a program to generate successive members of the look-and-say sequence.

See also

• Look-and-Say Numbers (feat John Conway), A Numberphile Video.
• This task is related to, and an application of, the Run-length encoding task.
• Sequence A005150 on The On-Line Encyclopedia of Integer Sequences.

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[edit]Ada

with Ada.Text_IO, Ada.Strings.Fixed;
use  Ada.Text_IO, Ada.Strings, Ada.Strings.Fixed;
 
function "+" (S : String) return String is
   Item : constant Character := S (S'First);
begin
   for Index in S'First + 1..S'Last loop
      if Item /= S (Index) then
         return Trim (Integer'Image (Index - S'First), Both) & Item & (+(S (Index..S'Last)));
      end if;
   end loop;
   return Trim (Integer'Image (S'Length), Both) & Item;
end "+";

This function can be used as follows:

Put_Line (+"1");
Put_Line (+(+"1"));
Put_Line (+(+(+"1")));
Put_Line (+(+(+(+"1"))));
Put_Line (+(+(+(+(+"1")))));
Put_Line (+(+(+(+(+(+"1"))))));
Put_Line (+(+(+(+(+(+(+"1")))))));
Put_Line (+(+(+(+(+(+(+(+"1"))))))));
Put_Line (+(+(+(+(+(+(+(+(+"1")))))))));
Put_Line (+(+(+(+(+(+(+(+(+(+"1"))))))))));

Output:

11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221

[edit]ALGOL 68

Translation of: Ada

Works with: ALGOL 68 version Standard - no extensions to language used

Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386

Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386

OP + = (STRING s)STRING:
BEGIN
   CHAR item = s[LWB s];
   STRING out;
   FOR index FROM LWB s + 1 TO UPB s DO
      IF item /= s [index] THEN
         out := whole(index - LWB s, 0) + item + (+(s [index:UPB s]));
         GO TO return out
      FI
   OD;
   out := whole (UPB s, 0) + item;
   return out: out
END  # + #;
 
OP + = (CHAR s)STRING: 
  + STRING(s);
 
print ((+"1", new line));
print ((+(+"1"), new line));
print ((+(+(+"1")), new line));
print ((+(+(+(+"1"))), new line));
print ((+(+(+(+(+"1")))), new line));
print ((+(+(+(+(+(+"1"))))), new line));
print ((+(+(+(+(+(+(+"1")))))), new line));
print ((+(+(+(+(+(+(+(+"1"))))))), new line));
print ((+(+(+(+(+(+(+(+(+"1")))))))), new line));
print ((+(+(+(+(+(+(+(+(+(+"1"))))))))), new line))

Output:

11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221

[edit]AutoHotkey

AutoExecute:    Gui, -MinimizeBox
    Gui, Add, Edit, w500 r20 vInput, 1
    Gui, Add, Button, x155 w100 Default, &Calculate
    Gui, Add, Button, xp+110 yp wp, E&xit
    Gui, Show,, Look-and-Say sequence
Return
 
 
ButtonCalculate:    Gui, Submit, NoHide
    GuiControl,, Input, % LookAndSay(Input)
Return