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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 05 2011
STATUS
approved