| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
This may look like just another "what's the next number?" puzzle, but there's a lot more to it. If there's enough interest, I'll tap in the good bits of an extraordinary short paper by J.H.Conway on the subject. So, what's the next in the sequence? 1 11 21 1211 111221 312211 ...? Or here's another example of the same process... 0 10 1110 3110 132110 1113122110 ...? And when you've worked out the pattern, the next question is: what's the long term behaviour of the sequence?
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 834.1 | 13112221 | VINO::JMUNZER | Thu Mar 03 1988 13:04 | 4 | |
I'd certainly be interested in seeing the "good bits". I have seen
the puzzle before.
John
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| 834.2 | 13211321322110 | CLT::GILBERT | Builder | Thu Mar 03 1988 16:41 | 2 |
Can a recognizer for either of these sets of generated strings be built with a finite-state machine, where scanning is allowed in either direction? | |||||
| 834.3 | Help! | AITG::DERAMO | Think of it as evolution in action. | Mon Mar 07 1988 11:53 | 4 |
I suppose the title was supposed to be a hint, but I don't get
it yet. How about another hint?
Dan
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| 834.5 | neato | AITG::DERAMO | Think of it as evolution in action. | Mon Mar 07 1988 15:44 | 16 |
>> Hint: Try describing each list out aloud, then writing it down.
Ohhhhhhhh, now I get it! [answer follows]
1 first string is arbitrary
11 because it follows: one 1
21 " two 1's
1211 " one 2, two 1's
111221 " one 1, one 2, two 1's
312211 " three 1's, two 2's, one 1
...?
So we would follow one 3, one 1, two 2's, two 1's with 13112221. (-:
Dan
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| 834.6 | uncommon digits | AKQJ10::YARBROUGH | Why is computing so labor intensive? | Tue Mar 15 1988 12:24 | 14 |
>Can a new digit 4 be created in a sufficiently old list? Only if it appears in the "seed" number, or the seed number contains 111 1's, or some other singular sequence. Otherwise, it would imply in the previous group two separate but adjacent collections of the same digit, which the formation rule precludes. In other words, "4" stems from something like "3333" which would have been written "63" instead. The same applies to any digit > 4. >Can the digits 333 occur in a sufficiently old list? Only if they appear in the original "seed" number. Otherwise, the existence of "333" implies that the same sequence appeared in the previous group, which leads to an infinite regression. | |||||
| 834.7 | a long time later | HERON::BUCHANAN | combinatorial bomb squad | Fri Feb 23 1990 13:52 | 445 |