mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2006-10-11, 15:53   #1
roger
 
roger's Avatar
 
Oct 2006

22·5·13 Posts
Default What's the next in the sequence?

1331; 12221; 112211; 145541; 167761; 201091

What's the next in the sequence, and how do you know?

PS - how do you black out text??
roger is offline   Reply With Quote
Old 2006-10-11, 16:25   #2
Xyzzy
 
Xyzzy's Avatar
 
"Mike"
Aug 2002

757310 Posts
Default

Use the [ spoiler ] tag.
Xyzzy is offline   Reply With Quote
Old 2006-10-11, 16:26   #3
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Rep├║blica de California

2×5,689 Posts
Default

My first guess was "ordered sequence of integers of the form a*b*c, where a,b,c are primes whose decimal expansion is of the form 1...1," but in that case your sequence is missing some terms.
ewmayer is offline   Reply With Quote
Old 2006-10-11, 16:40   #4
xilman
Bamboozled!
 
xilman's Avatar
 
May 2003
Down not across

27A716 Posts
Default

Quote:
Originally Posted by roger View Post
1331; 12221; 112211; 145541; 167761; 201091

What's the next in the sequence, and how do you know?

PS - how do you black out text??
42 because it is the answer to the ultimate question of life, the universe and everything.


Paul
xilman is online now   Reply With Quote
Old 2006-10-11, 17:32   #5
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

503 Posts
Default

This is pretty ambiguous but I have a few guesses


1)
347743 = 11*101*313
The previous three terms are multiples of 11*101 have 131,151 and 181 as high factors. 313 is the next palindromic prime after 181.

2)
1144411 = 11*101*10301
Same explanation as #1 above, except that only palindromic primes beginning and ending with 1 are allowed.

3)
188771 = 11*131*131
For the first 2 terms, the 2nd factor is 11. The next four, the 2nd factor is 101. So for the next 8 (or 6?) terms, the 2nd factor would be the next palindromic prime 101. The third factor would start with 131 and then skip to the next palindrome.

4)
1167216611 = 11 * 10301 *10301

Same explanation as #3, except that except that only palindromic primes beginning and ending with 1 are allowed.
grandpascorpion is offline   Reply With Quote
Old 2006-10-11, 22:32   #6
roger
 
roger's Avatar
 
Oct 2006

22·5·13 Posts
Default

To Grandpascorpion:

Your guess that the next in sequence would be the next palindromatic 'high' prime is correct. Honestly though, I didn't think someone would figure it out so quickly...

PS, thanks xyzzy
roger is offline   Reply With Quote
Old 2006-10-12, 01:55   #7
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

1111101112 Posts
Default

Roger, just curious, how did you come up with the first term? It doesn't really fit the rest of the sequence.
grandpascorpion is offline   Reply With Quote
Old 2006-10-12, 22:53   #8
roger
 
roger's Avatar
 
Oct 2006

4048 Posts
Default

Grandpascorpion,

The numbers were all the product of three palindromatic primes.

Since 1-digit numbers are only technically palindromatic, I started with 2-digit primes. 1331=11^3. Next is 11^2*101 (next palindromatic prime), then 11*101^2, 11*101*131, and so on up in size.
roger is offline   Reply With Quote
Old 2006-10-13, 00:25   #9
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

1111101112 Posts
Default

Sure, but couldn't the third term have been 11^2 * 103 instead of 11*101^2.

It seems a little arbitrary.
grandpascorpion is offline   Reply With Quote
Old 2006-10-13, 08:07   #10
xilman
Bamboozled!
 
xilman's Avatar
 
May 2003
Down not across

10,151 Posts
Default

Quote:
Originally Posted by grandpascorpion View Post
Sure, but couldn't the third term have been 11^2 * 103 instead of 11*101^2.

It seems a little arbitrary.
I'm missing something. 103 is palindromic?


Paul
xilman is online now   Reply With Quote
Old 2006-10-13, 09:07   #11
axn
 
axn's Avatar
 
Jun 2003

2×32×7×37 Posts
Default

Quote:
Originally Posted by xilman View Post
I'm missing something. 103 is palindromic?
Maybe he meant 131 ?

Last fiddled with by axn on 2006-10-13 at 09:08
axn is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Reserved for MF - Sequence 276 kar_bon Aliquot Sequences 97 2020-04-25 02:51
Primes in n-fibonacci sequence and n-step fibonacci sequence sweety439 And now for something completely different 17 2017-06-13 03:49
A new sequence devarajkandadai Math 1 2007-08-25 15:23
A New Sequence devarajkandadai Math 3 2007-03-20 19:43
Sequence Citrix Puzzles 5 2005-09-14 23:33

All times are UTC. The time now is 15:26.

Mon Aug 3 15:26:07 UTC 2020 up 17 days, 11:12, 1 user, load averages: 1.82, 2.50, 2.42

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.