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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

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Last modified August 11 03:41 EDT 2022. Contains 356046 sequences. (Running on oeis4.)