Comments on: Destinies of Numbers http://blog.tanyakhovanova.com/?p=155 Mathematics, applications of mathematics to life in general, and my life as a mathematician Tue, 07 Sep 2010 21:09:08 +0000 http://wordpress.org/?v=2.3 By: David Wilson http://blog.tanyakhovanova.com/?p=155#comment-12077 David Wilson Thu, 13 Aug 2009 03:08:39 +0000 http://blog.tanyakhovanova.com/?p=155#comment-12077 Maybe. Maybe.

]]> By: Tanya Khovanova http://blog.tanyakhovanova.com/?p=155#comment-12056 Tanya Khovanova Wed, 12 Aug 2009 22:45:29 +0000 http://blog.tanyakhovanova.com/?p=155#comment-12056 David, Great job! The second column is A161592. I expect you will submit your numbers to the OEIS. David,

Great job! The second column is A161592. I expect you will submit your numbers to the OEIS.

]]> By: David Wilson http://blog.tanyakhovanova.com/?p=155#comment-12035 David Wilson Wed, 12 Aug 2009 17:49:36 +0000 http://blog.tanyakhovanova.com/?p=155#comment-12035 I've found a few more elements of A161590, to wit 1 1 inf 3 111 8 9 117 2 29 1223 18 69 78 2 2079 111177 2 3999 11127 2 6999 11144445 14 10677 11667 2 20169 1111113 3 10049598 111111117777 2 20008989 111111777 2 100014888 1111122267 2 100074268 111122222255 6 The first column is A161590. The second column is the smallest element of the associated RATS cycle. The third column is A161593. For k >= 1, let x(k) be 2k 1's followed by k 7's, and y(k) = k 2's followed by 2k 8's. E.g: x1 = 117, y1 = 288 x2 = 111177, x2 = 228888 x3 = 111111777, x3 = 222888888 etc. The (x(k), y(k)) is a RATS cycle. This gives an infinite number of RATS cycles, each cycle must have a smallest number feeding it, so A161593 is infinite. I’ve found a few more elements of A161590, to wit

1 1 inf

3 111 8

9 117 2

29 1223 18

69 78 2

2079 111177 2

3999 11127 2

6999 11144445 14

10677 11667 2

20169 1111113 3

10049598 111111117777 2

20008989 111111777 2

100014888 1111122267 2

100074268 111122222255 6

The first column is A161590.

The second column is the smallest element of the associated RATS cycle.

The third column is A161593.

For k >= 1, let x(k) be 2k 1’s followed by k 7’s, and y(k) = k 2’s followed by 2k 8’s. E.g:

x1 = 117, y1 = 288
x2 = 111177, x2 = 228888
x3 = 111111777, x3 = 222888888
etc.

The (x(k), y(k)) is a RATS cycle. This gives an infinite number of RATS cycles, each cycle must have a smallest number feeding it, so A161593 is infinite.

]]>