|
| |
|
|
A185881
|
|
Trajectory of x^3+x+1 under the map (see A185544) defined in the Comments.
|
|
0
|
|
|
|
1011, 10011, 101111, 1001001, 10110110, 1011011, 10011011, 101111011, 1001001011, 10110110011, 100110111111, 1011110100001, 10010010010010, 1001001001001, 10110110110110, 1011011011011, 10011011011011, 101111011011011, 1001001011011011, 10110110011011011, 100110111111011011, 1011110100001011011
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Analogous to A185000 except start with x^3+x+1.
This trajectory is a rare example where it can be proved that the trajectory diverges.
We work in the ring GF(2)[x]. The map is f->f/x if f(0)=0, otherwise f->((x^2+1)f+1)/x. We represent polynomials by their vector of coefficients, high powers first. See A185544.
|
|
|
REFERENCES
|
J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 99.
|
|
|
LINKS
|
Table of n, a(n) for n=1..22.
Index entries for sequences related to 3x+1 (or Collatz) problem
|
|
|
EXAMPLE
|
The trajectory begins x^3+x+1, 1+x+x^4, x^5+x^3+x^2+x+1, x^6+x^3+1, x^7+x^4+x+x^5+x^2, x^6+x^3+1+x^4+x, 1+x+x^3+x^4+x^7, x+x^4+x^5+x^8+1+x^3+x^6, 1+x+x^3+x^6+x^9, x+x^4+x^7+x^10+1+x^5+x^8,
x^11+x^8+x^7+x^5+x^4+x^3+x^2+x+1, x^12+x^10+x^9+x^8+x^7+x^5+1, x+x^4+x^7+x^10+x^13,
x^12+x^9+x^6+x^3+1, ...
|
|
|
CROSSREFS
|
Cf. A185000, A185544.
Sequence in context: A345906 A035125 A183849 * A115769 A267613 A178396
Adjacent sequences: A185878 A185879 A185880 * A185882 A185883 A185884
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane, Feb 05 2011
|
|
|
STATUS
|
approved
|
| |
|
|
