37 lines
1.9 KiB
Text
37 lines
1.9 KiB
Text
The [[wp:Look and say sequence|Look and say sequence]] is a recursively defined sequence of numbers studied most notably by [[wp:John Horton Conway|John Conway]].
|
|
|
|
|
|
The '''look-and-say sequence''' is also known as the '''Morris Number Sequence''', after cryptographer Robert Morris, and the puzzle ''What is the next number in the sequence 1, 11, 21, 1211, 111221?'' is sometimes referred to as the ''Cuckoo's Egg'', from a description of Morris in Clifford Stoll's book ''The Cuckoo's Egg''.
|
|
|
|
|
|
'''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:
|
|
Write a program to generate successive members of the look-and-say sequence.
|
|
|
|
|
|
;Related tasks:
|
|
* [[Fours is the number of letters in the ...]]
|
|
* [[Number names]]
|
|
* [[Self-describing numbers]]
|
|
* [[Self-referential sequence]]
|
|
* [[Spelling of ordinal numbers]]
|
|
|
|
|
|
;See also:
|
|
* [https://www.youtube.com/watch?v=ea7lJkEhytA 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 [https://oeis.org/A005150 A005150] on The On-Line Encyclopedia of Integer Sequences.
|
|
<br><br>
|